N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation

Wen-Xiu Ma

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 270-279

Abstract: Within the Hirota bilinear formulation, we construct N-soliton solutions and analyze the Hirota N-soliton conditions in (2+1)-dimensions. A generalized algorithm to prove the Hirota conditions is presented by comparing degrees of the multivariate polynomials derived from the Hirota function in N wave vectors, and two weight numbers are introduced for transforming the Hirota function to achieve homogeneity of the related polynomials. An application is developed for a general combined nonlinear equation, which provides a proof of existence of its N-soliton solutions. The considered model equation includes three integrable equations in (2+1)-dimensions: the (2+1)-dimensional KdV equation, the Kadomtsev–Petviashvili equation, and the (2+1)-dimensional Hirota–Satsuma–Ito equation, as specific examples.

Keywords: N-soliton solution; Hirota N-soliton condition; (2+1)-dimensional integrable equations (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:270-279

DOI: 10.1016/j.matcom.2021.05.020

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