An implementation for the algorithm of Hirota bilinear form of PDE in the Maple system

DOI10.1016/j.amc.2006.06.034zbMath1110.65098OpenAlexW1982067987MaRDI QIDQ865524

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

Publication date: 19 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.06.034

zbMATH Keywords

numerical examplessymbolic computationnonlinear partial differential equationlogarithm transformationMaple package bilinearization

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Soliton equations (35Q51) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (6)

\textit{PDEBellII}: a Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations ⋮ 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 ⋮ A universal way to determine Hirota's bilinear equation of KdV type ⋮ Bilinearization

Uses Software

• CONSLAW
• Maple
• RATH
• WKPtest
• ATFM

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
• An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
• Symbolic computations of conserved densities for systems of nonlinear evolution equations
• A new algorithm for symbolic integration with application
• On soliton solutions of the Kaup-Kupershmidt equation. II: `Anomalous' \(N\)-soliton solutions
• Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
• Solitons and rational solutions of nonlinear evolution equations
• The Painlevé property for partial differential equations
• Soliton Solutions of a Coupled Modified KdV Equations
• Gauge symmetry and the generalization of Hirota's bilinear method

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