Inverse Scattering Method I. Methodological part with an example: Soliton solution of the Sine-Gordon Equation

TL;DR

This paper introduces the Inverse Scattering Method as a new approach for analyzing nonlinear dynamics, demonstrating its application by deriving the soliton kink solution of the Sine-Gordon Equation as an illustrative example.

Contribution

It presents the Inverse Scattering Method and applies it to explicitly obtain the soliton solution of the Sine-Gordon Equation, showcasing its utility in nonlinear problems.

Findings

Successfully derives the kink soliton solution using the inverse scattering approach

Provides a methodological framework for solving nonlinear equations

Illustrates the method with a well-known soliton example

Abstract

The aim of this paper is to introduce the Inverse Scattering Method for later studies of some problems in nonlinear dynamics, and describe the kink solution of the Sine Gordon Equation using the Inverse Scattering Method as a methodological example, the soliton solution is well known.