On integrability of variable coefficient nonlinear Schrodinger equations

TL;DR

This paper investigates the integrability of variable coefficient nonlinear Schrödinger equations using Painlevé analysis, providing explicit transformations to generate solutions and comparing methods for identifying integrable cases.

Contribution

It applies Painlevé test to classify integrable VCNLS equations and offers explicit solution-generating transformations, comparing with other integrability techniques.

Findings

Identified conditions for integrability of VCNLS equations.

Derived explicit transformations for solution generation.

Compared Painlevé analysis with other integrability methods.

Abstract

We apply Painlev\'e test to the most general variable coefficient nonlinear Schrodinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by the use of other tools like group-theoretical approach and the Lax pairs technique of the soliton theory. We present explicit transformation formulae that can be used to generate new analytic solutions of VCNLS equations from those of the integrable NLS equation.