HBHGen: a Maple package to construct the Hirota bilinear form for nonlinear equations

DOI10.1016/j.amc.2013.02.037zbMath1290.35003OpenAlexW2056013929MaRDI QIDQ2451440

Xu-Dong Yang, Hang-yu Ruan

Publication date: 3 June 2014

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

Full work available at URL: https://doi.org/10.1016/j.amc.2013.02.037

zbMATH Keywords

symbolic computationnonlinear partial differential equationHirota bilinear formlogarithm transformationmaple package

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Software, source code, etc. for problems pertaining to partial differential equations (35-04)

Related Items (4)

\textit{PDEBellII}: a Maple package for finding bilinear forms, bilinear Bäcklund transformations, Lax pairs and conservation laws of the KdV-type equations ⋮ Complexiton solutions for two nonlinear partial differential equations via modification of simplified Hirota method ⋮ Complexiton solutions for \((3+1)\) dimensional KdV-type equation ⋮ Multisoliton solutions and breathers for the coupled nonlinear Schrödinger equations via the Hirota method

Uses Software

• Maple
• MACSYMA
• HBFTrans2
• HBHGen
• HIROTA.MAX
• Bilinearization

Cites Work

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• Maple packages for computing Hirota's bilinear equation and multisoliton solutions of nonlinear evolution equations
• An implementation for the algorithm of Hirota bilinear form of PDE in the Maple system
• On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• 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
• Dromion-like structures in a (3+1)-dimensional KdV-type equation
• A search for bilinear equations passing Hirota’s three-soliton condition. IV. Complex bilinear equations
• Exact envelope-soliton solutions of a nonlinear wave equation

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