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Approach in theory of nonlinear evolution equations: the Vakhnenko–Parkes equation
Advances in Mathematical Physics, 2016
- Publisher
- Emerald Publishing
- Copyright
- © Emerald Publishing Limited
- ISSN
- 0961-5539
- DOI
- 10.1108/hff-09-2020-0560
- Publisher site
- See Article on Publisher Site
Abstract
This study aims to develop a new (3 + 1)-dimensional Painlevé-integrable extended Vakhnenko–Parkes equation. The author formally derives multiple soliton solutions for this developed model.Design/methodology/approachThe study used the simplified Hirota’s method for deriving multiple soliton solutions.FindingsThe study finds that the developed (3 + 1)-dimensional Vakhnenko–Parkes model exhibits complete integrability in analogy with the standard Vakhnenko–Parkes equation.Research limitations/implicationsThis study addresses the integrability features of this model via using the Painlevé analysis. The study also reports multiple soliton solutions for this equation by using the simplified Hirota’s method.Practical implicationsThe work reports extension of the (1 + 1)-dimensional standard equation to a (3 + 1)-dimensional model.Social implicationsThe work presents useful algorithms for constructing new integrable equations and for handling these equations.Originality/valueThe paper presents an original work with newly developed integrable equation and shows useful findings.
Journal
International Journal of Numerical Methods for Heat and Fluid Flow – Emerald Publishing
Published: May 24, 2021
Keywords: Vakhnenko–Parkes equation; Painlevé analysis; Compatibility conditions