Dynamics of transformed nonlinear waves for the (2+1)-dimensional pKP-BKP equation: interactions and molecular waves

Abstract

Abstract In this paper, the dynamical behaviors of transformed nonlinear waves for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili and B-type Kadomtsev-Petviashvili (pKP-BKP) equation are investigated, which can be used to reveal the nonlinear wave phenomena in nonlinear optics, plasma physics and hydrodynamics. The breath-wave and the lump solutions are constructed by means of the soliton solutions. The conversion mechanism for the breath-wave is systematically analyzed, which leads to several new kink-shaped nonlinear waves. The gradient relationships of these transformed waves are revealed by a Riemannian circle. Through the analysis of the nonlinear superposition between the periodic wave component and the kink solitary wave component, the dynamical characteristics including the formation mechanism, oscillation and locality for the nonlinear waves are investigated. The time-varying properties of transformed waves are shown by the study of time variables. By virtue of the two breath-wave solutions, several interactions including elastic and inelastic collisions between two nonlinear waves are studied. In particular, some transformed molecular waves encompassing the non-, semi- and full-transition modes are presented with the aid of velocity resonance. The results can help us further understand the complex nonlinear waves existing in the integrable systems.