Maple packages for computing Hirota's bilinear equation and multisoliton solutions of nonlinear evolution equations

DOI10.1016/j.amc.2010.05.012zbMath1205.65281OpenAlexW2012054414MaRDI QIDQ708138

Zhen-jiang Zhou, Jing-zhi Fu, Zhi-Bin Li

Publication date: 11 October 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.05.012

zbMATH Keywords

symbolic computationnonlinear evolution equationHirota bilinear methodsoliton solution\texttt{Maple}\texttt{Bilinearization}\texttt{Multisoliton}

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (10)

Propagation of traveling wave solutions to the Vakhnenko-Parkes dynamical equation via modified mathematical methods ⋮ \(N\)-soliton solutions and the Hirota conditions in (1 + 1)-dimensions ⋮ The \((G'/G)\)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation ⋮ Stability analysis and abundant closed-form wave solutions of the Date-Jimbo-Kashiwara-Miwa and combined sinh-cosh-Gordon equations arising in fluid mechanics ⋮ Collision and propagation of electromagnetic solitons in an antiferromagnetic spin ladder medium ⋮ An efficient algorithm of logarithmic transformation to Hirota bilinear form of KdV-type bilinear equation ⋮ Traveling wave solutions and infinite-dimensional linear spaces of multiwave solutions to Jimbo-Miwa equation ⋮ HBHGen: a Maple package to construct the Hirota bilinear form for nonlinear equations ⋮ EXPLICIT AND EXACT SOLUTIONS TO THE MODIFIED BENJAMIN-BONA-MAHONY EQUATION ⋮ A universal way to determine Hirota's bilinear equation of KdV type

Uses Software

• Maple
• RATH
• SYMMGRP
• MACSYMA
• HIROTA.MAX
• WKPtest

Cites Work

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• RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations
• Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple
• A new algorithm for symbolic integration with application
• Conservation laws and new exact solutions for the generalized seventh order KdV equation
• Symbolic software for soliton theory
• On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Solitons and rational solutions of nonlinear evolution equations
• A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
• A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations
• A search for bilinear equations passing Hirota’s three-soliton condition. III. Sine–Gordon-type bilinear equations
• Soliton Solutions of a Coupled Modified KdV Equations
• A search for bilinear equations passing Hirota’s three-soliton condition. IV. Complex bilinear equations

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