Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

Abstract

A large member of lump chain solutions of the (2 + 1)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation are constructed by means of the τ-function in the form of Grammian. The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities. An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains. The degenerate structures of parallel, superimposed, and molecular lump chains are presented. The interaction solutions between lump chains and kink-solitons are investigated, where the kink-solitons lie on the boundaries of dominant region determined by the constant term in the τ-function. Furthermore, the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated. The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.