Shapes and dynamics of dual-mode Hirota–Satsuma coupled KdV equations: Exact traveling wave solutions and analysis

Abstract

In this paper we communicated with three different ansatze methods including the tanh-expansion method, the rational sine–cosine method and the Kudryashov-expansion method to study solitary wave solutions for a new developed nonlinear equation. We presented new generalized Hirota–Satsuma coupled KdV system of second-order in time t involving phase-velocity, dispersion and nonlinearity parameters. The new system can be defined as a dual-mode model where each involved field-function possess a spreading of dual-waves instead of single-mode wave. Graphical illustrations on the effect of both phase-velocity and dispersion-nonlinearity factors on the spacing of the obtained dual-waves are provided.