An extended KdV6 hierarchy of nonlinear evolution equations: Painlevé integrability and variety of branches of resonances

Abstract

Purpose

The purpose of this paper is to study an extended hierarchy of nonlinear evolution equations including the sixth-order dispersion Korteweg–de Vries (KdV6), eighth-order dispersion KdV (KdV8) and many other related equations.

Design/methodology/approach

The newly developed models have been handled using the simplified Hirota’s method, whereas multiple soliton solutions are furnished using Hirota’s criteria.

Findings

The authors show that every member of this hierarchy is characterized by distinct dispersion relation and distinct resonance branches, whereas the phase shift retains the KdV type of shifts for any member.

Research limitations/implications

This paper presents an efficient algorithm for handling a hierarchy of integrable equations of diverse orders.

Practical implications

Multisoliton solutions are derived for each member of the hierarchy, and then generalized for any higher-order model.

Social implications

This work presents useful algorithms for finding and studying integrable equations of a hierarchy of nonlinear equations. The developed models exhibit complete integrability, by investigating the compatibility conditions for each model.

Originality/value

This paper presents an original work with a variety of useful findings.

Citation

Wazwaz, A.-M., Albalawi, W. and El-Tantawy, S.A. (2023), "An extended KdV6 hierarchy of nonlinear evolution equations: Painlevé integrability and variety of branches of resonances", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 2, pp. 673-681. https://doi.org/10.1108/HFF-06-2022-0385