Backlund transformation of Kaup Kupershmidt equations with mutli soliton solutions un Darboux framewor

TL;DR

This paper derives Darboux solutions and constructs Backlund transformations for Kaup Kupershmidt equations, providing multi-soliton solutions and their graphical profiles to reveal their dynamical behavior.

Contribution

It introduces a novel method to derive Backlund transformations for Kaup Kupershmidt equations using Riccati equations and Darboux solutions, including multi-soliton solutions.

Findings

Exact multi-soliton solutions up to three solitons obtained

Backlund transformations constructed via Riccati and Darboux methods

Graphical profiles illustrate the dynamical behavior of solutions

Abstract

This article encloses the derivation of Darboux solutions for Kaup Kupershmidt equations with their generalization in determinantal form. One of the main focuses of this work is to construct the Backlund transformation for the different solutions of that equation through its associated Riccati equation and then that transformations further reduces to its algebraic analogue with the help of One-fold Darboux solution. Finally, its exact solutions upto three solitons are calculated with their graphical representations which reveal dynamical profiles of these solutions.