Application of Darboux Transformation to solve Multisoliton Solution on Non-linear Schr\"odinger Equation

TL;DR

This paper applies Darboux transformation to derive explicit multisoliton solutions for the nonlinear Schrödinger equation, advancing analytical methods in nonlinear wave physics.

Contribution

It demonstrates how Darboux transformation can be used to obtain multisoliton solutions for the nonlinear Schrödinger equation from trivial initial conditions.

Findings

Explicit one to three soliton solutions derived

Method applicable to nonlinear-dispersive optical media

Enhances analytical solution techniques for nonlinear equations

Abstract

Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the nonlinear evolution equation. In this work, the evolution of monochromatic electromagnetic wave in a nonlinear-dispersive optical medium is considered. Using the Darboux transformation, explicit multisoliton solutions (one to three soliton solutions) are obtained from a trivial initial solution.