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

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.