Features of the interaction of paired solitary waves with the Cubic Vortical Whitham equation

Abstract

In this article, we consider the cubic vortical Whitham equation with both positive and negative nonlinearity to investigate overtaking solitary wave collisions. We compute solitary waves numerically, including “thick” solitary waves. Our results show that in both cases, the geometric Lax categorization holds, however, it is independent of the magnitude of the amplitude of the solitary waves. Besides, for negative cubic nonlinearity, we compute thick solitary waves and investigate their paired interactions. Moreover, we show that Gardner solitons and CV-Whitham solitary waves have nearly the same shape and speed when the sign of cubic nonlinearity term is negative.