Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system

TL;DR

This paper develops explicit solutions with non-trivial phase for inhomogeneous two-component nonlinear Schrödinger systems using Lie symmetry methods, expanding the class of known solutions with potential applications in physics.

Contribution

It introduces a novel application of Lie symmetry methods to construct explicit solutions with non-trivial phase for inhomogeneous coupled NLS systems, addressing a scarcely explored area.

Findings

Constructed new families of analytical solutions

Reduced the problem to integrability of a singular ODE

Provided illustrative examples of solutions

Abstract

In this article, we construct novel explicit solutions for nonlinear Schr\"odinger systems with spatially inhomogeneous nonlinearity by means of the Lie symmetry method. We focus the attention to solutions with non-trivial phase, which have been scarcely considered in the related literature. To get started, the theoretical method based on Lie symmetries is exposed, thus reducing the problem to the integrability of an ODE. The non-trivial phase introduces a singular term into the ODE. Then, the method is used to construct new families of analytical solutions. Some illustrative examples are provided.