New integrable Vakhnenko–Parkes (VP) equations with time-dependent coefficients

Abdul-Majid Wazwaz (Department of Mathematics, Saint Xavier University, Chicago, Illinois, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 24 June 2019

Abstract

Purpose

The purpose of this paper is concerned with developing new integrable Vakhnenko–Parkes equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the time-dependent equations.

Design/methodology/approach

The developed time-dependent models have been handled by using the Hirota’s direct method. The author also uses Hirota’s complex criteria for deriving multiple complex soliton solutions.

Findings

The developed integrable models exhibit complete integrability for any analytic time-dependent coefficient.

Research limitations/implications

The paper presents an efficient algorithm for handling time-dependent integrable equations with time-dependent coefficients.

Practical implications

The author develops two Vakhnenko–Parkes equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.

Social implications

The work presents useful techniques for finding integrable equations with time-dependent coefficients.

Originality/value

The paper gives new integrable Vakhnenko–Parkes equations, which give a variety of multiple real and complex soliton solutions.

Keywords

Citation

Wazwaz, A. (2019), "New integrable Vakhnenko–Parkes (VP) equations with time-dependent coefficients", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/HFF-04-2019-0358

Download as .RIS

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

Please note you might not have access to this content

You may be able to access this content by login via Shibboleth, Open Athens or with your Emerald account.
If you would like to contact us about accessing this content, click the button and fill out the form.