Partially invariant solutions of nonlinear Klein–Gordon and Laplace equations

DOI10.1063/1.529592zbMath0763.35081OpenAlexW2022543499MaRDI QIDQ4032263

Pavel Winternitz, Luigi Martina

Publication date: 1 April 1993

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

Full work available at URL: https://doi.org/10.1063/1.529592

zbMATH Keywords

reduction methodgroup analysissubgroup classification methods

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear elliptic equations (35J60) Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (5)

The reducibility of partially invariant solutions of systems of partial differential equations ⋮ On the solution of the nonlinear Schrödinger equation. ⋮ A differential constraints approach to partial invariance ⋮ Solutions of (2+1)-dimensional spin systems ⋮ Nonclassical symmetry reductions of the Boussinesq equation

Cites Work

• Automatically determining symmetries of partial differential equations
• Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation
• On the identification of a Lie algebra given by its structure constants. I: Direct decompositions, Levi decompositions, and nilradicals
• The computer calculation of Lie point symmetries of large systems of differential equations
• The construction of special solutions to partial differential equations
• Non-classical symmetry reduction: example of the Boussinesq equation
• Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups
• New similarity reductions of the Boussinesq equation
• Analysis of the three-dimensional time-dependent Landau-Ginzburg equation and its solutions
• Symmetry reduction for nonlinear relativistically invariant equations
• Group-Invariant Solutions of Differential Equations
• Symmetry breaking and bifurcating solutions in the classical complex ϕ⁶field theory
• Exact solutions of the multidimensional classical φ6-field equations obtained by symmetry reduction
• C-integrable nonlinear partial differentiation equations. I
• Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups

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