Bäcklund transformation and multi-soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries system via symbolic computation

DOI10.1016/j.amc.2009.06.001zbMath1203.35218OpenAlexW1979642568MaRDI QIDQ609286

Wen-Rui Shan, Tao Geng, Bo Tian, Xiang-Hua Meng

Publication date: 30 November 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.06.001

zbMATH Keywords

symbolic computationbilinear formBäcklund transformation\(N\)-soliton solution

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Software, source code, etc. for problems pertaining to partial differential equations (35-04) Soliton solutions (35C08) Methods of ordinary differential equations applied to PDEs (35A24)

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Cites Work

• Unnamed Item
• A new application of Riccati equation to some nonlinear evolution equations
• Symbolic computation on cylindrical-modified dust-ion-acoustic nebulons in dusty plasmas
• Darboux transformation and soliton solutions for Boussinesq-Burgers equation.
• Darboux and Bäcklund transformations for the nonisospectral KP equation
• A modified Bäcklund transformation and multi-soliton solution for the Boussinesq equation
• The Bäcklund transformation and novel solutions for the Toda lattice
• Bäcklund transformation in bilinear form for a higher-order nonlinear Schrödinger equation
• Soliton solutions and a Bäcklund transformation for a generalized nonlinear Schrödinger equation with variable coefficients from optical fiber communications
• Lax pair, Bäcklund transformation and \(N\)-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation
• Bäcklund transformation and soliton solutions for KP equation
• Chaos, solitons and fractals in \((2 + 1)\)-dimensional KdV system derived from a periodic wave solution
• Nonlinear Evolution Equations Generated from the Backlund Transformation for the Boussinesq Equation
• Simple Derivation of Backlund Transformation from Riccati Form of Inverse Method
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Bäcklund Transformation for the Exponential Lattice
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
• Painleve analysis of the non-linear Schrodinger family of equations
• Singularity analysis and localized coherent structures in (2+1)-dimensional generalized Korteweg–de Vries equations
• Generalized dromion solutions of the (2+1)-dimensional KdV equation
• Infinitely many Lax pairs and symmetry constraints of the KP equation
• Method for Solving the Korteweg-deVries Equation
• delta -dressing and exact solutions for the (2+1)-dimensional Harry Dym equation
• Abundant solitary wave structures of the nonlinear coupled scalar field equations