Transformations of ordinary differential equations via Darboux transformation technique

TL;DR

This paper introduces a novel method using Darboux transformations to generate solutions for nonlinear ordinary differential equations expressed as compatibility conditions of linear systems.

Contribution

It develops a new approach for transforming solutions of nonlinear ODEs via Darboux transformations, expanding the toolkit for solving such equations.

Findings

Derived transformations of solutions for nonlinear ODEs

Extended Darboux transformation techniques to new classes of equations

Provided a systematic method for solution generation

Abstract

A new approach for obtaining the transformations of solutions of nonlinear ordinary differential equations representable as the compatibility condition of the overdetermined linear systems is proposed. The corresponding transformations of the solutions of the overdetermined linear systems are derived in the frameworks of the Darboux transformation technique.