Localised Nonlinear Wave Interaction in the Generalised Kadomtsev-Petviashvili Equation

Abstract

The Hirota bilinear scheme and $τ$-function formalism is used in the study of localised nonlinear wave interaction structures generated by the six-soliton solutions of the generalised Kadomtsev-Petviashvili equation. Employing different sets of parameters and the long wave limit method, we consider examples of interaction of various types of waves — viz. line solitons, breathers and lumps. The dynamics of the corresponding interaction is demonstrated graphically to visualise the type of actions. The results obtained may be helpful in understanding the wave propagation in liquids containing gas bubbles.