Spectral problem for a two-component nonlinear Schr\"odinger equation in $2+1$ dimensions: Singular manifold method and Lie point symmetries
Exactly Solvable and Integrable Systems
2019-04-02 v1
Abstract
An integrable two-component nonlinear Schr\"odinger equation in 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 algebra. The main non-trivial similarity reductions associated to these symmetries are identified. The spectral parameter of the reduced spectral problem appears as a consequence of one of the symmetries.
Keywords
Cite
@article{arxiv.1807.09039,
title = {Spectral problem for a two-component nonlinear Schr\"odinger equation in $2+1$ dimensions: Singular manifold method and Lie point symmetries},
author = {Paz Albares and Juan Manuel Conde and Pilar García Estévez},
journal= {arXiv preprint arXiv:1807.09039},
year = {2019}
}