Multisoliton solutions via a separation of variables

TL;DR

This paper presents a novel method to derive multisoliton solutions of nonlinear PDEs using a separation of variables approach, linking solutions of a nonlinear ODE with linear PDEs.

Contribution

It introduces a unified separation of variables technique to generate multisoliton solutions across different nonlinear PDEs, highlighting a common nonlinear ODE structure.

Findings

Multisoliton solutions can be constructed from a shared nonlinear ODE.

The method applies to several well-known nonlinear PDEs.

A new link between nonlinear ODEs and linear PDEs is established.

Abstract

It is shown that multisoliton solutions of several well known nonlinear PDEs(x, t) can be obtained by certain separation of variables: each n-soliton arises from a mutual solution of a nonlinear ODE(x), common for all NPDEs considered, and linear PDE(x, t) with the linear operator from the NPDE in question.