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## Publications

Publications (13)

We present a generalized study and characterization of the integrability properties of the derivative non-linear Schrödinger equation in 1+1 dimensions. A Lax pair is derived for this equation by means of a Miura transformation and the singular manifold method. This procedure, together with the Darboux transformations, allow us to construct a wide...

We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciprocal KdV) and RmKdV (reciprocal mKdV), are connected through a transformation that combines both Miura and reciprocal transformations. Lax pairs for RKdV and RmKdV are strai...

The present work addresses the study and characterization of the integrability of three famous nonlinear Schr\"odinger equations with derivative-type nonlinearities in 1+1 dimensions. Lax pairs for these three equations are successfully obtained by means of a Miura transformation and the singular manifold method. After implementing the associated b...

We present a generalized study and characterization of the integrability properties of the derivative non-linear Schr\"odinger equation in 1+1 dimensions. A Lax pair is derived for this equation by means of a Miura transformation and the singular manifold method. This procedure, together with the Darboux transformations, allow us to construct a wid...

An integrable two-component nonlinear Schrödinger equation in 2+1 dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional Lie a...

Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the identification of a plethora of partial differential equations that are spread out in the physics and mathematics literatu...

An integrable two-component nonlinear Schr\"odinger equation in $2+1$ dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair. The Lie point symmetries of this Lax pair are calculated in terms of nine arbitrary functions and one arbitrary constant that yield a non-trivial infinite-dimensional L...

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the...

A non-isospectral linear problem for an integrable 2+1 generalization of the non linear Schrödinger equation, which includes dispersive terms of third and fourth order, is presented. The classical symmetries of the Lax pair and the related reductions are carefully studied. We obtain several reductions of the Lax pair that yield in some cases non-is...

We investigate the generalized (2+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2+1)$$\end{document} Nizhnik–Novikov–Veselov equation and construct its linear eige...

In this paper an effective integrable non-linear model describing the electron spin dynamics in a deformable helical molecule with weak spin-orbit coupling is presented. Non-linearity arises from the electron-lattice interaction and it enables the formation of a variety of stable solitons such as bright solitons, breathers and rogue waves, all of t...

It is widely admitted that the helical conformation of certain chiral molecules may induce a sizable spin selectivity observed in experiments. Spin selectivity arises as a result of the interplay between a helicity-induced spin-orbit coupling and electric dipole fields in the molecule. From the theoretical point of view, different phenomena might a...