Transcendental surface wave to the symmetric regularized long-wave equation

Abstract

The symmetric regularized long-wave (SRLW) equation describes the attribute of the nonlinear ion acoustic waves, space charge waves, undular bore in meteorology etc. In this article, we investigate the SRLW equation to rummage transcendental shape of surface wave solution using the auxiliary equation approach and the improved Bernoulli sub-equation function technique. The solutions are ascertained in the form of trigonometric, hyperbolic, rational and exponential functions containing several ascendant parameters to the SRLW equation through the stated approaches which are compatible, dependable and simple to use. We extract a variety of rich structured surface solitons from the generic solution obtained including parabolic, kink, bell-shaped, lump soliton, etc. The implications of the various parameter values associated with the resulting solution are explicitly discussed to demonstrate their importance in explaining wave profiles behavior which may be convenient for analyzing nonlinear ion acoustic wave and space charge waves.