On the symmetry groups of the intrinsic generalized wave and sine–Gordon equations

DOI10.1063/1.530042zbMath0780.35102OpenAlexW1970377971MaRDI QIDQ3141357

Keti Tenenblat, Pavel Winternitz

Publication date: 6 February 1994

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.530042

zbMATH Keywords

exact invariant solutionsintrinsic generalized sine-Gordon equationintrinsic generalized wave equationLie-point symmetry groups

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) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (5)

Submanifolds of constant sectional curvature in pseudo-Riemannian manifolds ⋮ Invariant solutions for the static vacuum equation ⋮ A (2+1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solutions ⋮ Recursion operator for the intrinsic generalized sine-Gordon equation ⋮ Reduction of the \(n\)-dimensional static vacuum Einstein equation and generalized Schwarzschild solutions

Cites Work

• The inverse scattering solution for the full three dimensional three-wave resonant interaction
• A higher dimension generalization of the Sine-Gordon equation and its soliton theory
• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• Equations différentielles du second ordre en Y et du second degré en Y dont l'intégrale générale est à points critiques fixes
• Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem
• On the Solution of the Generalized Wave and Generalized Sine-Gordon Equations
• Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra
• On the infinite-dimensional symmetry group of the Davey–Stewartson equations
• Solutions of the nonlinear 3-wave equations in three spatial dimensions
• Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation
• Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations
• On three-dimensional packets of surface waves

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