Emmanuel Kengne

Zhejiang Normal University (China) & University of Quebec at Outaouais (Canada) · College of Mathematics Physics and Information Engineering (China) & Department of Computer Sciences and Engineering (Canada)

A coupled cubic nonlinear Schrödinger (NLS) equations with external potentials in normal dispersion regimes is considered. Combining the phase engineering technique with a modified lens transformation, the integrability condition is derived and the equations are reduced to an integrable Kundu-Eckhaus (KE) equation that always admits rogue wave solu...

Multi-coupled equations of Gross-Pitaevskii type that model binary (two-component) BECs are considered. Employing various analytical techniques such as the technique of Darboux transform (DT), exact analytical soliton solutions are presented. With the help of these soliton solutions, we investigate analytically the soliton management and stability...

In this chapter, we analytical discuss the transmission of modulated rogue waves through electric nonlinear transmission networks when the losses are either neglected or taken into consideration. For a given electrical model of the nonlinear transmission network, we employ the reductive perturbation method in the semi-discrete limit to reduce the d...

Using the mapping techniques, we investigate analyticallyBose-Einstein condensates the dynamics of rogue matter waves in Bose-Einstein condensates trapped in time-varying external potentials. Rational solutions of the model equations are presented and used to engineer first-order and second-order matter rogue waves Rogue waves in the BEC contexts w...

This chapter deals with the dynamics of one-dimensional Bose-Einstein condensate models with varying scattering length trapped in time-dependent external potentials. Through the Gross-Pitaevskii equations with either the cubic or cubic-quintic nonlinearities, we apply diverse methods and techniques such as the direct method (DM), the ansatz method...

In the present chapter, we investigate the dynamics of nonlinear modulated waves propagating along multi-coupled electric transmission networks. The dynamics of slowly modulated waves propagating through different network systems are reduced to either two-dimensional higher order (HO) NLS equationsNLS equation or generalized two-dimensional complex...

This chapter presents analytical results for the dynamics of nonlinear modulated waves in dissipative electrical nonlinear transmission networks. We employ the reductive perturbation method in the semi-discrete limit to derive a dissipative NLS equation that models the propagation of nonlinear modulated waves in the given network. Based on both the...

We consider in this chapter a (non)integrable system of three nonlinearly coupled GP equation, which describes the dynamics of matter-wave solitons in a three-component spinor Bose-Einstein condensate. One-, two-, and three-component soliton solutions of the polar and ferromagnetic (FM) typesMatter-waves are presented. ApplyingBose-Einstein condens...

In this Chapter, we consider the lossless 1DLossless NLTN discrete dispersive NLTNNLTNs sketched in Fig. 2.1. When lattice effects are considered, the reductive perturbation method in the semi-discrete limit can be used to show that the dynamics of modulatedNonlinear transmission network waves can be modeled by PDEs of Schrödinger type, which descr...

The present Chapter deals generally with more general nonintegrable models, and particularly, with higher-order GP equations, that may model the dynamics of higher-dimensional Bose-Einstein condensates. These models are treated by means of both the variational approximation (VA) and direct computational simulations. We mainly focus our attention on...

This Chapter focuses on the dynamics of magnetization in ferromagnetSpin-transfer torque described by the generalized Landau–Lifshitz–Gilbert equation. By means of HirotaLandau–Lifshitz–Gilbert equations bilinear method (HBM), exact analytical single- and two-soliton solutions of the model equation are presented. Using these solutions, we investiga...

In this chapter, we consider a number ofMagnetic solitons mathematical models which describe various nonlinear phenomena, including the dynamics of dissipative magnetic matter-wave solitons in a spinor polariton Bose-Einstein condensate, nonlinear magnetization dynamics (NMDs) of the classical ferromagnet with two single-ion anisotropies in an exte...

The purpose of this work is to illustrate by clear examples the noetherity nature of a finite Dirac-delta Extensions of a studied noether operator. Previously in our published papers, we have investigated in different two cases, the noetherization of a Dirac-delta extensions of a noether linear integro-differential operator defined by a third kind...

We consider a model of three-core PIM-NIM-PIM coupler with Kerr-type saturable non-linearity to study both analytically and numerically saturation effects on the modulational instability (MI) phenomenon. The analytical results show us that, in presence of saturable parameters in normal and anomalous dispersion regime the instability gain presents s...

Inspired by standard electrophysiological models of microtubules (MTs), we consider a relatively large one-dimensional spatial array of nonlinear electrical transmission network with a negative nonlinear resistance. Employing the reductive perturbation approach in the semi-discrete approximation, we show that the evolution of ionic waves in this el...

A dissipative nonlinear transmission net work is studied in the regular regime using both ana lytical approach and numerical technique that allow us to obtain the stable and unstable periodic orbits of this network in a systematic way. Going from a one dimensional Ginzburg-Landau equation that governs the dynamics of modulated waves in the network...

A two-dimensional nonlinear discrete electric transmission network made of several well-known anharmonic modified Noguchi lines coupled transversely to one another with a linear inductor is considered and the dynamics of modulated waves are investigated. The linear analysis shows that increasing either the dispersive elements of the network, the co...

Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great va�riety of physical settings, such as nonlinear photonics, dynamical phase transitions, superconductivity, superfluidity, hydrodynamics, plasmas, Bose–Einstein condensates, liquid crystals, field-theory strings, etc. This article provides a review of one- and two�dimensio...

This work deals with the engineering dissipative chirped solitary waves in the cardiac tissue under electromagnetic induction. Employing the a two-dimensional Ginzburg-Landau (GL) equation describing the spatiotempo-ral evolution of transmembrane potential in cardiac cells under magnetic flow effect, we use the phase imprint technique to reduce the...

The main goal of this work is to establish the extension of a noether operator defined by a third kind singular integral equation in a special class of generalized functions and to investigate the noetherity of the extended operator. The initial considered operator has been investigated for its noetherity nature in our previous works. Special appro...

In virus dynamics, when a cell is infected, the number of virions outside the cells is reduced by one: this phenomenon is known as absorption effect. Most mathematical in intra-host models neglects this phenomenon. Virus-to-cell infection and direct cell-to-cell transmission are two fundamental modes whereby viruses can be propagated and transmitte...

We consider a model of three-core PIM-NIM-PIM coupler with Kerr-type saturable nonlinearity to study both analytically and numerically saturation effects on the modulational instability phenomenon. The analytical results show us that, in presence of saturable parameter in normal and anomalous dispersion regime it is formed some new instability band...

We investigate the modulational instability phenomenon and demonstrate that the competing cubic-quintic nonlinearity induces propagating solitonlike bright (dark) solitons, first-order rogue waves embedded on a continuous wave background, and two sister modulated waves in the nonlinear Schrö dinger equation with self-steepening and self-frequency s...

We examine a third kind integral equation in the class of generalized functions. We show that the considered equation has similar solvability properties as the Fredholm equation of the second kind.

The basic need common to all living beings is water. Less than 1% of the water on earth is fresh water and water use is increasing daily. Agricultural practices alone require huge amounts of water. The drip technique improved the efficiency of water use in irrigation and initiated the introduction and development of fertigation, the integrated dist...

We consider a cubic Gross-Pitaevskii (GP) equation governing the dynamics of Bose-Einstein condensates (BECs) with time-dependent coefficients in front of the cubic term and inverted parabolic potential. Under a special condition imposed on the coefficients, a combination of phase-imprint and modified lens-type transformations converts the GP equat...

The present paper investigates the spatiotemporal evolution of a population of mesenchymal cells during invasion. In that end, a mathematical model accounting for haptotaxis, chemotaxis, zero-proliferation, viscous, and traction forces is considered. Injecting plane wave ansatz in the model reveals viscoelastic properties of the medium, as well as...

We consider a cubic Gross-Pitaevskii (GP) equation governing the dynamics of Bose-Einstein condensates (BECs) with time-dependent coefficients in front of the cubic term and inverted parabolic potential. Under a special condition imposed on the coefficients, a combination of phase-imprint and modified lens-type transformations converts the GP equat...

We consider the one-dimensional (1D) cubic-quintic Gross–Pitaevskii (GP) equation, which governs the dynamics of Bose–Einstein condensate matter waves with time-varying scattering length and loss/gain of atoms in a harmonic trapping potential. We derive the integrability conditions and the compensation condition for the 1D GP equation and obtain, w...

The dynamics of spatiotemporal modulated damped signals in a nonlinear LC transmission network with dissipative elements are investigated analytically. The complex cubic Ginzburg–Landau (GL) equation governing slowly modulated wave propagation is presented. Considering linear wave propagating in the network, we derive in terms of the propagating fr...

In a recent paper (Elsayed et al., 2021), authors introduce the coupled system of magneto-optics waveguides for the nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index. Using the unified auxiliary equation method, they construct, in terms of Jacobi elliptic function, mathematical solutions to this system. In some limit cases...

We investigate analytically the dynamics of modulated waves in an alternate right-handed and left-handed multi-coupled nonlinear dissipative discrete electrical lattice, made of several of the well-known modified Noguchi electrical transmission network that are transversely coupled to one another by a linear capacitor C 2. The damped two dimensiona...

A discrete nonlinear transmission network with dispersive element is considered. It is shown that the dynamics of slowly modulated waves propagating in this network are governed by a generalized cubic‐quintic nonlinear Schrödinger equation with self‐steepening and self‐frequency shift. Through the baseband modulational instability (MI) analysis, th...

The dynamics of modulated waves in a nonlinear discrete transmission network with dissipative elements are investigated analytically. The generalized cubic-quintic Ginzburg-Landau (GCQ-GL) equation with intrapulse Raman scattering (IRS) terms governing spatially damped slowly modulated wave propagation is derived. Considering modulated Stokes wave...

We consider the one-dimensional (1D) cubic-quintic Gross--Pitaevskii (GP)nequation, which governs the dynamics of Bose--Einstein condensate (BEC) matter waves with time-varying scattering length and loss/gain of atoms in a harmonic trapping potential. We derive the integrability conditions and the compensation condition for the 1D GP equation and o...

In this work, we consider the generalized cubic-quintic dissipative Gross-Pitaevskii equation, which governs the dynamics of matter wave solitons in Bose-Einstein condensates (BECs) with two- and three-body interatomic interactions in a spatiotemporal-dependent dissipative potential consisting of parabolic, linear, and complex terms. By using the a...

Since the realization of Bose-Einstein condensates (BECs) in optical potentials, intensive experimental and theoretical investigations have been carried out for matter-wave solitons, coherent structures, modulational instability (MI), and nonlinear excitation of BEC matter waves, making them objects of fundamental interest in the vast realm of nonl...

Since the realization of Bose–Einstein condensates (BECs) trapped in optical potentials, intensive experimental and theoretical investigations have been carried out for bright and dark matter-wave solitons, coherent structures, modulational instability (MI), and nonlinear excitation of BEC matter waves, making them objects of fundamental interest i...

A modified Noguchi nonlinear electric transmission network that consists of a large number of identi- cal sections is theoretically studied in the present work. A new capacitance-voltage (C-V) characteristics of the diodes containing a square root nonlinearity is introduced and used to show that in the contin- uum limit, the voltage for the transmi...

By introducing a suitable ansatz and employing the similarity transformation technique, we construct the first- and second-order rational solutions for a quasi-one-dimensional (1D) dissipative Gross–Pitaevskii (GP) equation with a time-varying cubic nonlinearity and an external time-dependent potential. Then, by using these solutions, we engineer f...

A one-dimensional modified Nogochi nonlinear electric transmission network with dispersive elements that consist of a large number of identical sections is theoretically studied in the present paper. The first-order nonautonomous rogue waves with quintic nonlinearity and nonlinear dispersion effects in this network are predicted and analyzed using...

Controlled thermal ablation in order to maximize the therapy and minimize the side effects poses a challenge during the heating of the biological tissue. Traditionally, these processes are modelled by the bio heat equation introduced by Pennes, who used the Fourier's theory of heat conduction. During my talk I will present our automated thermal dos...

The amplitude modulation of ion-acoustic waves is investigated in a plasma system consisting of ions and electrons obeying κ-distribution. Taking into account the dissipative mechanisms that consist of the ionization and applying a reductive perturbation technique, a one-parameter dissipative nonlinear Schrödinger (DNLS) equation of electrostatic p...

Based on a modified one-dimensional Noguchi electrical transmission network containing a linear dispersive element CS with a voltage source and a one-dimensional series capacitor transmission network, we build a two-dimensional nonlinear discrete electrical network which allow the wave propagation in both the longitudinal and the transverse directi...

In the small amplitude limit, we use the reductive perturbation method and the continuum limit approximation to derive a coupled nonlinear Schrö dinger (CNLS) equation describing the dynamics of two interacting signal packets in a discrete nonlinear electrical transmission line (NLTL) with linear dispersion. With the help of the derived CNLS equati...

We show that the methodology based on the powerful method of the so-called hidden symmetry reductions (HSR) provides a systematic way to analytically derive non-autonomous temporal soliton solutions of a one-dimensional inhomogeneous nonlinear Schrödinger equation with a linear gain or loss, a linear density profile, and distributed dispersion. The...

A distributed electrical transmission network with dispersive elements that consists of a large number of identical unit cells is considered. Using the reductive perturbation method in the semidiscrete limit, we show that the voltage for the network is described by a nonlinear Schrödinger (NLS) equation with an external linear potential. Using such...

To investigate the dynamical behaviors of multi-species Bose–Einstein condensates in an optical lattice, we consider, in this chapter, the multicomponent nonlinear Schrödinger type equations. We successively study the phase diagram for superfluid and insulator phases of two-species BECs in a one-dimensional optical lattice, the vector solitons and...

Based on the inhomogeneous cubic–quintic nonlinear Schrödinger equation with external real or complex potential, we investigate in this chapter the dynamics of Bose–Einstein condensates when both the two- and three-body interatomic interactions are taken into consideration. We start by performing different methods leading to the exact analytical pe...

The present chapter deals with an overview of nonlinear Schrödinger equations that are mainly used to investigate the dynamics of nonlinear matter waves of either the nonlinear transmission networks or the Bose–Einstein condensates: The one-dimensional cubic nonlinear Schröodinger equations including the standard and the dissipative cases, the deri...

Based on the higher dimensional inhomogeneous nonlinear Schrödinger equations with external real/complex potential, we investigate in this chapter the dynamics of BECs in external potentials. A special attention will be paid on the both analytical and numerical studies of (i) BECs with both two- and three-bodies interactions, loaded into a 2D harmo...

This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the...

In the present chapter, we study the generation of nonlinear modulated waves in one-dimensional real electrical lattices. In the continuum limit, we use the semi-discrete approximation to show that the dynamics of modulated waves through the networks under considerations are governed by derivative equations of Schrödinger type including the general...

Questions related to the well-posedness of differential problems in the mathematical modeling of real objects, phenomena, and processes form are essential and very important part of problems of the description of real objects by mathematical means. Mathematically, a given boundary-value problem is said to be well-posed (in Hadamard sense) if (a) a...

This chapter investigates the dynamics of modulated waves through the system of the nonlinear transmission lines coupled by a linear capacitor. We prove that the dynamics of modulated waves through the system under consideration are governed by either a 2D NLS equation or a 2D NLS system. Based on these equations, we analytically investigate the tr...

A single-component BEC is typically well-described by a scalar order parameter, the BEC wave function, whose dynamics are governed by a one-component nonlinear Schrödinger equation with an external potential. Atomic BECs with internal spin degrees of freedom (spinor condensates) offer a new form of coherent matter with complex internal quantum stru...

The present chapter deals with a time-dependent inhomogeneous cubic nonlinear Schrödinger equation with external real/complex potential which at ultralow temperatures, describes the time-dependent wavefunction of the Bose–Einstein condensates when only the two-body interatomic interactions are taken into account. Through the analytical investigatio...

In this chapter, we use the multicomponent nonlinear Schrödinger equations to investigate the dynamics of spin–orbit coupling (SOC) in Bose–Einstein condensates. We will study the rotating spin-1 BECs with anisotropic SOC, the spin texture of the vortex chain for rotating spin-1 BECs, the spin singularity phenomenon in the spin-1 BECs, the topologi...

The present chapter deals with the investigation of the dynamics of modulated waves propagating through a modified single nonlinear transmission network in both cases when the second-neighbor interactions are neglected and when the second-neighbor interactions are taken into account. Using the reductive perturbation approach in the semidiscrete app...

An innovative approach based on the biochip technology for real-time monitoring of a thermal therapy applied in oncology is proposed in this paper. The proposed system provides two primary functions: real-time tracking of the targeted tissue’s thermal diffusion while at the same time locally characterizes and provides the parameters of the tissue....

In this paper, we consider a Gross-Pitaevskii (GP) equation with a time-dependent nonlinearity and a spatiotemporal complex linear term which describes the dynamics of matter-wave solitons in Bose-Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms. We establi...

A modified lossless nonlinear Noguchi transmission network with second-neighbor interactions is considered. In the semidiscrete limit, we apply the reductive perturbation method and show that the dynamics of modulated waves propagating through the network are governed by an NLS equation with linear external potential. Classes of exact solitonic sol...

To analytically investigate the matter-wave solitons of Bose–Einstein condensates (BECs) in time-dependent complex potential, we consider a cubic-quintic Gross–Pitaevskii (GP) equation with distributed coefficients and a dissipative term. By introducing a suitable ansatz, we establish the criterion of the modulational instability (MI) of the system...

In the present study, an axisymmetric one-dimensional Pennes bioheat transfer model is used to investigate analytically the heat transport in the peripheral region of a human limb undergoing healing after surgery. The analytical exact solution to the model is presented in terms of modified Bessel functions. Through the found analytical solution, th...

Thermal therapy is a promising treatment for many patients particularly those with surgery intolerance. It has been used since the early age of humanity. Nowadays, the thermal therapy has proved its efficacy, especially in Oncology. In fact, the tumor ablation using a different modality of heating or cooling presents a therapeutic method to ablate...

The Hardware Implementation of the physical models offers an outstanding opportunity for engineers in computational computing techniques. Contrary to the software implementation, the physical hardware implementations present the advantage of speed up the computation with inexpensive and practical way. The Finite Difference Method (FDM) is one the m...

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

A lossless nonlinear LC transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. A...

This paper presents a new method for determining the exact number of inverters in one ring oscillator of temperature sensors that must be used optimally to monitor and control a complex system design. This method is very efficient, simple and easy to implement. The proposed temperature sensor was designed using TSMC 65 nm CMOS technology, which occ...

The objective of this work is to make a thermal study beginning with the simulation and implementation of the equation of thermal convection in a complex system design through numerical simulation. This simulation is based on the code of the numerical calculation by finite element module CFD that will allow us to model a variety of physical phenome...

Controlled thermal ablation poses a challenge during a laser surgery/cancer treatment. A software tool would help physicians predict, organize the treatment as well as maximize therapeutic effects while minimizing side effects. This would provide a precise idea of the predicted reaction depending on selected doses, tissue geometry, and the laser so...

In the present work, we study the generation of nonlinear modulated waves in a modified version of Noguchi electrical tr ansmission network. In the continuum limit, we have considered the semi discrete approximation and showed that wave modulations in the network are governed by a generalized Chen-Lee-Liu (G-CLL) equation whose “self steepening” pa...

A 3D Finite Element Method (FEM) model for directional removing of a tumor is presented in this paper. The proposed model shows a new method to control the direction of the temperature diffusion during the thermal ablation. We developed a directional probe with a curved cathode as heating source to remove the malignant cells and protect the surroun...

In this present paper, we investigate analytically the dynamics of modulated waves in a dissipative nonlinear network with nonlinear dispersion. In the small amplitude limit, we use the reductive perturbation method and the continuum limit approximation to derive an envelope Ginzburg-Landau (GL) equation of the network. Considering modulated Stokes...

We investigate the dynamics of matter-wave solitons in the one-dimensional (1-D) Gross-Pitaevskii (GP) equation describing Bose-Einstein condensates (BECs) with time-dependent scattering length in varying trapping potentials with feeding/loss term. By performing a modified lens-type transformation, we reduce the GP equation into a classical nonline...

Due to the restriction of the number of probes that a patient can tolerate and the inaccurate information provided by the invasive temperature measurements, which provide information only at discrete points, a mathematical model simulation is more effective to help physicians in planning their thermal treatment doses. This simulation will maximize...

Motivated by recent experimental investigations in the context of matter wave solitons in BoseEinstein condensates (BECs), we consider the 1+1 Gross-Pitaevskii equation with complex time-varying harmonic potential, and time-varying cubic and quintic nonlinearities. By performing a modified lens type transformation for the one-dimensional GP equatio...

We study analytically the dynamics of modulated waves in a dissipative modified Noguchi nonlinear electrical network. In the continuum limit, we use the reductive perturbation method in the semidiscrete limit to establish that the propagation of modulated waves in the network is governed by a dissipative nonlinear Schr¨odinger (NLS) equation. Motiv...