Multisolitons in the surface gravity waves and internal waves

Abstract

In this paper, a five-order Korteweg–de Vries (KdV) equation is studied, which is used to describe the nonlinear phenomena in the fluids, especially those of the surface gravity waves and internal waves in the stratified fluids. (a) Via the symbolic calculation, this KdV equation cannot pass the Painlevé test without any constraint conditions. By virtue of the ansatz method, bell-shape and kink soliton solutions of this KdV equation are attained. (b) Via the bilinear method, multisoliton solutions of this KdV equation are obtained under some constraint conditions. Propagation and interaction of the multisoliton are discussed. Soliton interaction is elastic, that is to say, they have no effect on each other’s amplitude and speed except for phase shift. We hope that our results will be useful for experimental studies of surface gravity waves and internal waves since the coefficients of this KdV equation are all expressed in terms of physical constants, depths, and densities of the fluid.