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

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.