Interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation for nonlinear waves

Abstract

• A generalized bilinear equation is proposed and linked with a nonlinear model describing nonlinear wave in fluids and oceans. • Two types of interaction solution (lump-kink and lump-soliton) have been derived, based on which rogue wave may be predicted. • Completely non-elastic interaction between lump and stripe has been presented (the lump is drowned/shallowed by the stripe). • Interaction between lump and soliton has been given (lump moves from one branch to the other branch of the soliton). • These phenomena exhibit the dynamical process of nonlinear waves and are useful to study the nonlinear interaction behavior. In this paper, we focus on the interaction behavior associated with a generalized (2+1)-dimensional Hirota bilinear equation. With symbolic computation, two types of interaction solutions including lump-kink and lump-soliton ones are derived through mixing two positive quadratic functions with an exponential function, or two positive quadratic functions with a hyperbolic cosine function in the bilinear equation. The completely non-elastic interaction between a lump and a stripe is presented, which shows the lump is drowned or shallowed by the stripe. The interaction between lump and soliton is also given, where the lump moves from one branch to the other branch of the soliton. These phenomena exhibit the dynamics of nonlinear waves and the solutions are useful for the study on interaction behavior of nonlinear waves in shallow water, plasma, nonlinear optics and Bose–Einstein condensates.