Multiple-soliton solutions for the ninth-order KdV equation and sixth-order Boussinesq equation

Abstract

Two nonlinear dispersive equations, namely, the ninth-order KdV equation and the sixth-order Boussinesq equation, are formally derived by generalizing the bilinear forms of the KdV and Boussinesq equations, respectively. The two equations are approached by using the tanh–coth method to obtain single soliton solutions, and by the Hirota bilinear method, to determine the multiple-soliton solutions. The study highlights the fact that both equations are completely integrable and admits N-soliton solutions.