The \((2+1)\)-dimensional Konopelchenko-Dubrovsky equation: nonlocal symmetries and interaction solutions

DOI10.1007/s11071-016-2998-4zbMath1371.35004OpenAlexW2526874888WikidataQ56907648 ScholiaQ56907648MaRDI QIDQ2407582

Ji Lin, Bo Ren, Xue-Ping Cheng

Publication date: 6 October 2017

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-016-2998-4

zbMATH Keywords

symmetry reductionnonlocal symmetriesKonopelchenko-Dubrovsky equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Symmetries, invariants, etc. in context of PDEs (35B06)

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Cites Work

• Unnamed Item
• Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation
• Generalized (2 + 1)-dimensional Gardner model: bilinear equations, Bäcklund transformation, Lax representation and interaction mechanisms
• Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation
• The periodic wave solutions for the \((2 + 1)\)-dimensional Konopelchenko-Dubrovsky equations
• Nonlocal symmetries of evolution equations
• Symmetry and integration methods for differential equations
• Symbolic computation and new families of exact soliton-like solutions of Konopelchenko-Dubrov\-sky equations
• Soliton fission and fusion: Burgers equation and Sharma-Tasso-Olver equation
• Nonlocal symmetry and exact solutions of the \((2+1)\)-dimensional breaking soliton equation
• Further improved F-expansion method and new exact solutions of Konopelchenko--Dubrovsky equation
• New bilinear Bäcklund transformation with multisoliton solutions for the (2+1)-dimensional Sawada-Kotera model
• Integration of the soliton hierarchy with self-consistent sources
• On the Relation between Lie Symmetries and Prolongation Structures of Nonlinear Field Equations: Non-Local Symmetries
• Nonlocal symmetries related to Bäcklund transformation and their applications
• Interactions Between Solitons and Cnoidal Periodic Waves of the (2+1)-Dimensional Konopelchenko—Dubrovsky Equation
• Framework for potential systems and nonlocal symmetries: Algorithmic approach
• The Painlevé property for partial differential equations
• Rigorous bounds on the power spectrum of arbitrary prime eta -order renormalisation group equations
• Negative Kadomtsev–Petviashvili Hierarchy
• Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations
• Nonlocal symmetries of the KdV equation
• Nonlocal Symmetry Reductions, CTE Method and Exact Solutions for Higher-Order KdV Equation
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy
• Finite Symmetry Transformation Groups and Exact Solutions of Konopelchenko–Dubrovsky Equation

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