Lyapunov-Schmidt reduction in the study of bifurcation of periodic travelling wave solutions of a perturbed (1 + 1)−dimensional dispersive long wave equation

Abstract

In this paper, the Lyapunov-Schmidt reduction is used to investigate the bifurcation of periodic travelling wave solutions of a perturbed (1+1)−dimensional dispersive long wave equation. We demonstrate that the bifurcation equation corresponding to the original problem is supplied by a nonlinear system of two cubic algebraic equations. As the bifurcation parameters change, this system has only one, three, or five regular real solutions. The linear approximation of the solutions to the main problem has been discovered.