Soliton solutions by means of Hirota bilinear forms

Wen-Xiu Ma

Partial Differential Equations in Applied Mathematics (Jun 2022)

Soliton solutions by means of Hirota bilinear forms

Wen-Xiu Ma

Affiliations

Wen-Xiu Ma: Correspondence to: Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA.; Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China; Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia; Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA; School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

Journal volume & issue: Vol. 5
p. 100220

Abstract

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The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various integrable equations. The Hirota conditions for N-soliton solutions are analyzed and a few open questions regarding higher-dimensional cases and generalized bilinear equations are presented.

Published in Partial Differential Equations in Applied Mathematics

ISSN: 2666-8181 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods
Website: https://www.journals.elsevier.com/partial-differential-equations-in-applied-mathematics

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