A series of new analytical solutions to the nonlinear equation y t+y x x x−6y2y x+6λy x=0. I

Abstract

Following the Bäcklund transformation and using the theorems proved by the same authors, previously we obtained sets of new solutions to the KdV equation and the nonlinear equation yt+yxxx−6y2yx +6λyx=0 which transforms into the modified KdV equation when λ=0. In this paper we present another new series of solutions to the above nonlinear equation. One of our analytical solutions under a certain special condition (vacuum parameter b=0 and λ=0) is found to be identical to the one-soliton solution obtained via the inverse scattering method.