Generalized gauge transformation approach to construct dark solitons of coupled nonlinear Schrodinger type equations

TL;DR

This paper introduces a purely algebraic gauge transformation method to construct dark solitons in coupled nonlinear Schrödinger equations, with potential applications in optics, plasma physics, and Bose-Einstein condensates.

Contribution

The paper presents a novel algebraic approach using gauge transformations to generate dark solitons in coupled NLS equations, expanding tools for nonlinear wave analysis.

Findings

Successfully constructed dark solitons for coupled GP and NLS equations.

Method applicable to vector dark solitons in various physical fields.

Potential for broader application in nonlinear wave research.

Abstract

We harness the freedom in the celebrated gauge transformation approach to generate dark solitons of coupled nonlinear Schr\"odinger (NLS) type equations. The new approach which is purely algebraic could prove to be very useful, particularly in the construction of vector dark solitons in the fields of nonlinear optics, plasma physics and Bose-Einstein condensates. We have employed this algebraic method to coupled Gross- Pitaevskii (GP) and NLS equations and obtained dark solitons.