## About

83

Publications

10,631

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,940

Citations

Citations since 2016

## Publications

Publications (83)

In this paper we consider two-dimensional (2D) rogue waves that can be obtained from the approximate solution of the (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation with Kerr nonlinearity. The approximate method proposed in this paper not only reduces complex operations needed for the solution of high-dimensional nonlinear partial differen...

We found a new family of non-diffracting Laguerre beams, which are constructed by the associated Laguerre polynomials and trigonometric functions, and described by different radial mode numbers and negative topological charges. Surprisingly, the description with negative topological charges is very different from the description of the general non-...

This paper investigates new rogue wave solutions of the nonlinear Schrödinger equation with variable coefficients, utilizing the self-similar transformation method. A new rogue wave family is introduced, which displays different wave structures. When one chooses appropriate variable coefficients, a series of first-order, second-order, and third-ord...

This paper investigates diffraction-free Laguerre-Gaussian solutions of the two-dimensional paraxial wave equation in linear media, which are described by the radial and angular mode numbers, and constitute some diffraction-free polygon beams, constructed through the linear superposition principle. By selecting appropriate values of the two mode nu...

In this paper, the propagation characteristics of three-dimensional spatiotemporal nondiffracting parabolic cylinder beams in free space are studied. From the (3+1)-dimensional paraxial wave equation, we obtain an exact solution by the method of separating variables. The solution is constructed using parabolic cylinder functions, described by the t...

We find asymmetric diffraction-free Laguerre-Gaussian solutions of the two-dimensional paraxial wave equation in free space. They are constructed by the Laguerre polynomials and trigonometric functions, and described by the radial and angular mode numbers, and modulation depth. Different optical field distributions of the asymmetric diffraction-fre...

We investigate the two-dimensional normalized linear Schrödinger equation describing the propagation of diffraction-free beams in free space using the traditional variable separation method. We discover that each beam component satisfies the standard Weber differential equation. From this fact, we construct exact solutions utilizing two parabolic c...

We find a new class of Airy beams by combining in a distichous fashion two two-dimensional (2D) Airy beams propagating as counter-accelerating beams. To explore their unique characteristics, the distichous 2D Airy beams are constructed, their rotation factor is introduced, and the spatial distribution of their intensity when the rotation factor is...

The first- and second-order breather solutions of the self-focusing nonlocal nonlinear Schrödinger (NNLS) equation are obtained by employing Hirota's bilinear method. The NNSE also happens to be an example of Schrödinger equation with parity-time (PT) symmetry. With the help of recurrence relations in the Hirota bilinear form, the nth-order breathe...

A class of self-similar beams, named three-dimensional (3D) spatiotemporal parabolic accessible solitons, are introduced in the 3D highly nonlocal nonlinear media. We obtain exact solutions of the 3D spatiotemporal linear Schrödinger equation in parabolic cylindrical coordinates by using the method of separation of variables. The 3D localized struc...

In this paper, the dynamics of dark solitons in inhomogeneous self-defocusing Kerr-media are explored by utilizing the nonlinear Schrödinger (NLS) equation with variable coefficients. Firstly, the mathematical model with variable coefficients is simplified to the standard NLS equation with constant coefficients, by using the self-similar transforma...

We explore novel excitations in the form of nonlinear local waves, which are described by the sinh-Gordon (SHG) equation with a variable coefficient. With the aid of the self-similarity transformation, we establish the relationship between solutions of the SHG equation with a variable coefficient and those of the standard SHG equation. Then, using...

The propagation of finite energy Airy beams in dynamic parabolic potentials, including uniformly moving, accelerating, and oscillating potentials, is investigated. The propagation trajectories of Airy beams are strongly affected by the dynamic potentials, but the periodic inversion of the beam remains invariant. The results may broaden the potentia...

An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the \((2+1)\)-dimensional (D) sine-Gordon (SG) equation...

In this paper, we investigate the (2+1)-dimensional (D) sine-Gordon (SG) equation, to describe the propagation of localized light waves in nonlinear media. The main purpose is to obtain a simple specific form of exact solutions of the (2+1)-D SG equation by Hirota’s bilinear method. The novel dynamical behavior is discussed systematically for some...

A scheme for realizing Thirring vector solitons is proposed, with the help of giant Kerr nonlinearity and electromagnetically induced transparency in an atomic gas system. Generic Thirring vector solitons, formed by the distributed nonlinearity coupling and loss (or gain) coefficients, are constructed analytically, using the homogeneous balance pri...

We demonstrate both theoretically and experimentally diffraction-free propagation and self-accelerating properties of linear spatiotemporal Airy-Bessel wave packets. We show that these beams display two distinct profiles: zero-vorticity rings and vortex beams for zero and integer topological charges, respectively. The experimental observations agre...

The (3+1)‐dimensional [(3+1)D] nonlinear Schrödinger (NLS) equation is investigated, describing the propagation of nonlinear spatiotemporal wave packets in a self‐defocusing medium, and a new type of Airy spatiotemporal solutions is presented. By using the reductive perturbation method, the (3+1)D NLS equation is reduced to the spherical Kortewegde...

Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting t...

By using the modified Snyder-Mitchell (MSM) model, which can describe the propagation of a paraxial beam in fractional dimensions (FDs), we find the exact "accessible soliton” solutions in the strongly nonlocal nonlinear media with a self-consistent parity-time (PT) symmetric complex potential. The exact solutions are constructed with the help of t...

We investigate the control of dark ring solitons with multi-layer ring-shapes, which are the one- and two-soliton solutions of the Korteweg-de Vries (KdV) equation. By using the reductive perturbation method, a cylindrical KdV equation for the two-dimensional self-defocusing nonlinear Schrödinger (NLS) equation is obtained, which possesses dark sol...

Dark three-dimensional spatiotemporal solitons or the “dark light bullets” in the self-defocusing nonlinear media with equal diffraction and dispersion lengths are demonstrated analytically. Our results show that the main characteristic of the dark light bullets can be described by the cylindrical Korteweg–de Vries (CKdV) equation. The dark wave pa...

We report solutions for solitons of the "accessible" type in globally nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped modes in the space of effective dimension $2<D\le3$ with harmonic-oscillator potential whose strength is proportional to the total power of the wave field. The solutions are categorized by a combination...

The pioneering paper 'Optical rogue waves' by Solli et al (2007 Nature
450 1054) started the new subfield in optics. This work launched a great deal of activity on this novel subject. As a result, the initial concept has expanded and has been enriched by new ideas. Various approaches have been suggested since then. A fresh look at the older result...

Exact solution of the (3+1)D Schrödinger-type equation without external potential is obtained in cylindrical coordinates by using the method of separation of variables. Linear compressed light bullets are constructed with the help of a superposition of two counter-accelerating finite Airy wave functions and the Tricomi-Gaussian polynomials. We pres...

We construct rogue waves (RWs) in a coupled two-mode system with the
self-focusing nonlinearity of the Manakov type (equal SPM and XPM
coefficients), spatially modulated coefficients, and a specially designed
external potential. The system may be realized in nonlinear optics and
Bose-Einstein condensates. By means of a similarity transformation, we...

We demonstrate three-dimensional (3D) Airy-Laguerre-Gaussian localized wave packets in free space. An exact solution of the (3 + 1)D potential-free Schrödinger equation is obtained by using the method of separation of variables. Linear compressed wave pulses are constructed with the help of a superposition of two counter-accelerating finite energy...

We construct self-decelerating Airy-Bessel linear light bullet solutions of the three-dimensional potential-free Schrödinger equation, and present their spatiotemporal profiles. In the analysis, three different possibilities for the topological charge (TC) are considered: (i) TC is zero, (ii) TC is integer, and (iii) TC is half-integer. In addition...

Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the soluti...

A new special two-soliton solution to the generalized Sine–Gordon equation with a variable coefficient is constructed analytically, by using the self-similar method and Hirota bilinear method. To construct this special solution, we do not utilize the pairs of one-soliton solutions, as is customarily done when solving the Sine–Gordon equation, but i...

We present a class of exact solutions to the coupled (2 + 1)-dimensional nonlinear Schrodinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functio...

We demonstrate controllable parabolic-cylinder optical rogue waves in certain inhomogeneous media. An analytical rogue wave solution of the generalized nonlinear Schrödinger equation with spatially modulated coefficients and an external potential in the form of modulated quadratic potential is obtained by the similarity transformation. Numerical si...

We investigate the propagation of localized three-dimensional spatiotemporal Airy self-accelerating parabolic-cylinder light bullets in a linear medium. In particular, we consider the effects resulting from utilizing initial finite-energy Airy wave packets to accelerate these localized beams in the absence of any external potential. A general local...

We demonstrate azimuthally modulated resonance scalar and vector solitons in self-focusing and self-defocusing materials. They are constructed by selecting appropriately self-consistency and resonance conditions in a coupled system of multicomponent nonlinear Schrödinger equations. In the case with zero modulation depth, it was found that the large...

A similarity transformation is utilized to reduce the generalized nonlinear Schrödinger (NLS) equation with variable coefficients to the standard NLS equation with constant coefficients, whose rogue wave solutions are then transformed back into the solutions of the original equation. In this way, Ma breathers, the first- and second-order rogue wave...

Using multivariate self-similarity transformation, we construct explicit spatial bright and dark solitary wave solutions of the generalized nonlinear Schrödinger equation with spatially Bessel-modulated nonlinearity and an external potential. Special kinds of explicit solutions, such as periodically breathing bright and dark solitary waves, are dis...

We study analytically and numerically 'accessible' spatiotemporal solitons in a three-dimensional strongly nonlocal nonlinear medium. A general localized soliton solution of the 'acceptable' type is obtained in the Cartesian coordinates, using even and odd parabolic-cylinder functions. Characteristics of these accessible spatiotemporal solitons are...

New solitary and extended wave solutions of the generalized sinh-Gordon (SHG) equation with a variable coefficient are found by utilizing the self-similar transformation between this equation and the standard SHG equation. Two arbitrary self-similar functions are included in the known solutions of the standard SHG equation, to obtain exact solution...

We introduce three-dimensional (3D) spatiotemporal vector solitary waves in coupled (3+1)D nonlinear Schrödinger equations with variable diffraction and nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing for novel localized solutions. Using the Hirota bilinear method, 3D approximate but analytical spatiotempo...

Utilizing the three-dimensional Snyder-Mitchell model with a PT-symmetric potential, we study the influence of PT symmetry on beam propagation in strongly nonlocal nonlinear media. The complex Coulomb potential is used as the PT-symmetric potential. A localized spatiotemporal accessible soliton solution of the model is obtained. Specific values of...

Two-dimensional parity-time (PT) symmetric potentials are introduced, which allow the existence of spatial solitons in the model of the strongly nonlocal nonlinear Schrödinger equation. Two-dimensional accessible solitons are found in the form of solutions separating the radial amplitude, given in terms of Laguerre polynomials, a phase function inv...

By using the self-similar method for obtaining localized solutions of nonlinear evolution partial differential equations, we found analytical breather solutions to the nonlinear Schrödinger equation with longitudinally variable coefficients and an arbitrary transversely linear potential. The Ma and the second-order breather solutions are derived by...

We report on the localized spatial soliton excitations in the multidimensional nonlinear Schrödinger equation with radially variable nonlinearity coefficient and an external potential. By using Hirota's binary differential operators, we determine a variety of external potentials and nonlinearity coefficients that can support nonlinear localized sol...

We analytically investigated two-dimensional localized nonlinear waves in Kerr media with radial and azimuthal modulation of the nonlinearity and in the presence of an external potential. The solutions have been derived through the similarity transformation. We demonstrate that the properties of nonlinear waves are determined by two parameters: a w...

We report approximate analytical solutions to the (3+1)-dimensional spatiotemporal nonlinear Schrödinger equation, with the uniform self-focusing nonlinearity and a variable negative radial diffraction coefficient, in the form of three-dimensional solitons. The model may be realized in artificial optical media, such as left-handed materials and pho...

We demonstrate "hidden solvability" of the nonlinear Schrödinger (NLS) equation whose nonlinearity coefficient is spatially modulated by Hermite-Gaussian functions of different orders and the external potential is appropriately chosen. By means of an explicit transformation, this equation is reduced to the stationary version of the classical NLS eq...

An improved self-similar transformation is used to construct exact so-lutions of the nonlinear Schrödinger equation with variable nonlinearity and quadratic external potential, which both depend on the distance of propagation and the transverse spatial coordinate. By means of analytical and numerical methods we reveal the main features of the spati...

We report solutions for expanding dipole-type optical solitary waves in two-dimensional Kerr media with the self-focusing nonlinearity, using exact analytical (Hirota) and numerical methods. Such localized beams carry intrinsic vorticity and exhibit symmetric shapes for both scalar and vector solitary modes. When vector beams are close to the scala...

We investigate three-dimensional (3D) spatiotemporal vector solitary waves in spherical coordinates. The exact 3D analytical nonstationary (slowly expanding) solutions are obtained by the separation of variables and the Hirota bilinear method. Novel 3D spatiotemporal vector solitary waves are built with the help of spherical harmonics include multi...

Applying Hirota's binary operator approach to the (2+1)-dimensional nonlinear Schrödinger equation with the radially variable diffraction and nonlinearity coefficients, we derive a variety of exact solutions to the equation. Based on the solitary wave solutions derived, we obtain some special soliton structures, such as the embedded, conical, circu...

We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septi...

We construct a class of three-dimensional strongly nonlocal spatiotemporal solitary waves of the nonlocal nonlinear Schrödinger equation, by using superpositions of single accessible solitons as initial conditions. Evolution of such solitary waves, termed the accessible light bullets, is studied numerically by choosing specific values of topologica...

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is id...

We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schrödinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare wit...

Two-dimensional accessible solitary wave families of the
generalized nonlocal nonlinear Schrödinger equation are obtained by
utilizing superpositions of various single accessible solitary solutions.
Specific values of soliton parameters are selected as initial conditions and
the superposition of known single solitary solutions in the highly nonloca...

We study analytically and numerically the propagation of spatial solitons in a two-dimensional strongly nonlocal nonlinear medium. Exact analytical solutions in the form of self-similar spatial solitons are obtained involving higher-order Hermite–Gaussian functions. Our theoretical predictions provide new insights into the low-energy spatial solito...

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such...

We present beam solutions of the strongly nonlocal nonlinear
Schrödinger equation in left-handed materials (LHMs). Different
Laguerre-Gaussian (LG) necklace beams, such as symmetric and asymmetric
single layer and multilayer necklace beams are created by the
superposition of two single beams with different topological charges.
Such superpositions a...

Exact extended traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Gross-Pitaevskii equation with time-dependent coefficients are obtained. The case with constant diffraction and parabolic potential strength, but with variable gain, is discussed in some detail. It is found that gain in the system is necessary fo...

The evolution of traveling and solitary waves in Bose-Einstein condensates (BECs) with a time-dependent scattering length in an attractive/repulsive parabolic potential is studied. The homogeneous balance principle and the F-expansion technique are used to solve the one-dimensional Gross-Pitaevskii equation with time-varying coefficients. We obtain...

A generic nonlocal nonlinear optical system with a diffusive type of nonlinearity is investigated analytically, using the
homogeneous balance principle and the F-expansion technique. Exact traveling wave and soliton solutions are discovered. Numerical
simulation of their propagation and interaction properties is carried out. Our results demonstrate...

Bright and dark matter wave solitons are
constructed analytically in a three-dimensional (3D) highly anisotropic
Bose-Einstein condensate (BEC) with a time-dependent parabolic potential,
and numerical simulations are performed to confirm the existence and
dynamics of such analytical solutions. Different classes of bright and dark
solitons are disco...

We obtain exact extended traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equations for both the normal and the anomalous dispersion.

We investigate, analytically and numerically, a class of novel higher-order spatial solitons in two transverse-dimensions,
in highly nonlocal nonlinear media. The stability of these solutions in propagation is confirmed by direct numerical simulation.
Our results demonstrate that the higher-order spatial solitons in highly nonlocal nonlinear media...

We study the propagation of spatial solitons in nematic liquid crystals, using the self-similar method. Analytical solutions in the form of self-similar solitons are obtained exactly. We confirm the stability of these solutions by direct numerical simulation, and find that the stable spatial solitons can exist in various forms, such as Gaussian sol...

A systematic density functional study has been performed on the structural, electronic and spectroscopic properties of C50X12 (X = H, F, Cl, Br). Nine types of carbon atoms and two kinds of X (X = H, F, Cl, Br) atoms are found in these four C-50 (D-3) derivatives, which are all well distinguished by C-13 NMR spectra signals. C50X12 (X = F, Cl, Br)...

We demonstrate the existence of localized optical vortex and necklace
solitons in three-dimensional (3D) highly nonlocal nonlinear media, both
analytically and numerically. The 3D solitons are constructed with the
help of Kummer’s functions in spherical coordinates and their
unique properties are discussed. The procedure we follow offers ways for
g...

We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spa...

Collisions of spatial solitons occurring in the nonlinear Schröinger equation with harmonic potential are studied, using conservation laws and the split-step Fourier method. We find an analytical solution for the separation distance between the spatial solitons in an inhomogeneous nonlinear medium when the light beam is self-trapped in the transver...

We obtain exact spatiotemporal periodic traveling wave solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients. We utilize these solutions to construct analytical light bullet soliton solutions of nonlinear optics.

DOI:https://doi.org/10.1103/PhysRevA.78.039905