26 citations · 67 across the 10 of their papers we have counts for
10 papers
Spectral problem for the complex mKdV equation: singular manifold method and Lie symmetries
Paz Albares, Pilar G. Estévez, Alejandro González-Parra +1
This article addresses the study of the complex version of the modified Korteweg-de Vries equation using two different approaches. Firstly, the singular manifold method is applied…
Miura-reciprocal transformation and symmetries for the spectral problems of KdV and mKdV
Paz Albares, Pilar García Estévez
We present reciprocal transformations for the spectral problems of Korteveg de Vries (KdV) and modified Korteveg de Vries (mKdV) equations. The resulting equations, RKdV (reciproca…
Integrability and rational soliton solutions for gauge invariant derivative nonlinear Schrödinger equations
Paz Albares
The present work addresses the study and characterization of the integrability of three famous nonlinear Schrödinger equations with derivative-type nonlinearities in 1+1 dimensions…
Derivative non-linear Schrödinger equation: Singular manifold method and Lie symmetries
Paz Albares, Pilar García Estévez, Juan Domingo Lejarreta
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 t…
Reciprocal transformations and their role in the integrability and classification of PDEs
P. Albares, P. G. Estévez, C. Sardón
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized vers…
Spectral problem for a two-component nonlinear Schrödinger equation in dimensions: Singular manifold method and Lie point symmetries
Paz Albares, Juan Manuel Conde, Pilar García Estévez
An integrable two-component nonlinear Schrödinger equation in dimensions is presented. The singular manifold method is applied in order to obtain a three-component Lax pair.…
Classical Lie symmetries and reductions for a generalized NLS equation in 2+1 dimensions
P. Albares, J. M. Conde, P. G. Estévez
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 presente…
Chiral solitons in a non-linear model of helical molecules
P. Albares, E. Diaz, J. M. Cervero +3
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-linear…
Spin dynamics in helical molecules with non-linear interactions
E. Diaz, P. Albares, P. G. Estevez +4
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 o…
Lumps and Rogue waves of Generalized Nizhnik Novikov Veselov Equation
P. Albares, P. G. Estevez, R. Radha +1
We investigate the generalized (2 + 1) Nizhnik-Novikov-Veselov equation and construct its linear eigenvalue problem in the coordinate space from the results of singularity structur…