Controllable Transformed Waves of a (2+1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation in Fluids

Abstract

In this paper, the dynamical behaviors of transformed nonlinear waves for a (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation are investigated, which can be used to reveal the nonlinear wave phenomena in shallow water and ion-acoustic waves in fluid dynamics. Using the Hirota’s bilinear method, the N-soliton solutions can be obtained. By adding complex conjugation conditions, the breather wave solutions can be formed. Breather waves can be converted into various kinds of nonlinear waves under some restrictive conditions, such as quasi-solitons, quasi-periodic waves, multi-peak solitons, W-shaped solitons, oscillating M-shaped solitons and parabolic waves. By virtue of the higher-order breather wave solutions, the interactions of long-lived and short-lived collisions between two nonlinear waves are studied. In particular, based on the condition of velocity resonance, the dynamics of unidirectional and reciprocating molecular waves are discussed. The results contribute to a deeper understanding of the complex nonlinear wave phenomena existing in integrable systems.