Classical Lie symmetries and reductions for a generalized NLS equation in 2+1 dimensions

TL;DR

This paper investigates classical Lie symmetries of a 2+1 dimensional generalized nonlinear Schrödinger equation, deriving reductions that connect to lower-dimensional non-isospectral problems, enhancing understanding of its integrability and symmetry structure.

Contribution

It provides a detailed analysis of symmetries and reductions for a complex 2+1D NLS generalization, including non-isospectral problems, which was not previously explored.

Findings

Identified classical symmetries of the Lax pair.

Derived reductions leading to 1+1D non-isospectral problems.

Enhanced understanding of the integrability structure of the generalized NLS equation.

Abstract

A non-isospectral linear problem for an integrable 2+1 generalization of the non linear Schr\"odinger 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-isospectral problems in 1+1 dimensions.