Two wave mode higher-order modified KdV equations: Essential conditions for multiple soliton solutions to exist

Abstract

Purpose

The purpose of this paper is concerned with developing two-mode higher-order modified Korteweg-de Vries (KdV) equations. The study shows that multiple soliton solutions exist for essential conditions related to the nonlinearity and dispersion parameters.

Design/methodology/approach

The proposed technique for constructing a two-wave model, as presented in this work, has been shown to be very efficient. The employed approach formally derives the essential conditions for soliton solutions to exist.

Findings

The examined two-wave model features interesting results in propagation of waves and fluid flow.

Research limitations/implications

The paper presents a new and efficient algorithm for constructing and studying two-wave-mode higher-order modified KdV equations.

Practical implications

A two-wave model was constructed for higher-order modified KdV equations. The essential conditions for multiple soliton solutions to exist were derived.

Social implications

The work shows the distinct features of the standard equation and the newly developed equation.

Originality/value

The work is original and this is the first time for two-wave-mode higher-order modified KdV equations to be constructed and studied.

Citation

Wazwaz, A.-M. (2017), "Two wave mode higher-order modified KdV equations: Essential conditions for multiple soliton solutions to exist", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 10, pp. 2223-2230. https://doi.org/10.1108/HFF-10-2016-0413