Nonlocal symmetries and explicit solutions of the Boussinesq equation

DOI10.1007/s11401-014-0868-2zbMath1304.35577OpenAlexW2047979333MaRDI QIDQ475835

Junchao Chen, Yong Chen, Xiang-Peng Xin

Publication date: 27 November 2014

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-014-0868-2

zbMATH Keywords

explicit solutionLax pairnonlocal symmetryprolonged system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Local Lie groups (22E05) Soliton solutions (35C08)

Related Items (5)

Nonlocal symmetry and consistent Riccati expansion integrability of the (1+1)-dimensional integrable nonlinear dispersive-wave system ⋮ Consistent Riccati expansion solvability and soliton-cnoidal wave interaction solution of a \((2 + 1)\)-dimensional Korteweg-de Vries equation ⋮ CRE solvability and soliton-cnoidal wave interaction solutions of the dissipative \((2+1)\)-dimensional AKNS equation ⋮ Nonlocal symmetries and explicit solutions for the Gardner equation ⋮ Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation

Cites Work

• Symmetry reduction and exact solutions of the generalized Nizhnik-Novikov-Veselov equation
• Nonlocal symmetries and the theory of coverings: An addendum to A. M. Vinogradov's 'Local Symmetries and Conservation Laws'
• Applications of symmetry methods to partial differential equations
• Nonlocal symmetries. Heuristic approach
• Two new applications of the homogeneous balance method
• Extended tanh-function method and its applications to nonlinear equations
• Nonlocal symmetries related to Bäcklund transformation and their applications
• Wronskian solutions of the Boussinesq equation—solitons, negatons, positons and complexitons
• Framework for potential systems and nonlocal symmetries: Algorithmic approach
• New similarity reductions of the Boussinesq equation
• New classes of symmetries for partial differential equations
• New nonlocal symmetries with pseudopotentials
• Conformal invariance and integrable models
• More non-local symmetries of the KdV equation
• Soliton on a cnoidal wave background in the coupled nonlinear Schrödinger equation
• Non-local symmetries via Darboux transformations
• The fourth Painlevé equation and associated special polynomials
• Rational Solutions of Painlevé Equations
• Symmetries and differential equations
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