Darboux Transformation for Drinfel'd–Sokolov–Wilson Equation

Abstract

A coupled system known as the Drinfel'd–Sokolov–Wilson equation is reexamined. With the help of a Lax operator of fourth order, its proper Darboux transformation is constructed. Also, a nonlinear superposition formula is worked out for the associated Bäcklund transformation and some solutions are calculated.

Construction of soliton and multiple soliton solutions to the longitudinal wave motion equation in a magneto-electro-elastic circular rod and the Drinfeld-Sokolov-Wilson equation

“…To study of the model is given by [40] re-examined the well known coupled system as the DSW equation. Its proper Darboux transformation is constructed with the help of a Lax operator of fourth order and some solutions are calculated and a nonlinear superposition formula is worked out for the associated Backlund transformation.…”