On the general solution of the d’Alembert equation with a nonlinear eikonal constraint and its applications

DOI10.1063/1.531142zbMath0849.35021OpenAlexW2097385504MaRDI QIDQ4873429

I. V. Revenko, Renat Zhdanov, W. I. Fushchich

Publication date: 16 April 1996

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

Full work available at URL: https://semanticscholar.org/paper/ae50df305dc8e4e86f0c16f72d2527712b437bdd

zbMATH Keywords

nonlinear d'Alembert equation

Mathematics Subject Classification ID

Nonlinear higher-order PDEs (35G20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Solutions to PDEs in closed form (35C05)

Related Items (3)

Conditional symmetry and spectrum of the one-dimensional Schrödinger equation ⋮ Compatibility criteria and general solution of the nonlinear d'Alembert-eikonal system ⋮ A precise definition of reduction of partial differential equations

Cites Work

• General solutions of the nonlinear wave equation and of the eikonal equation
• On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system
• Null field solutions of the wave equation and certain generalizations
• New similarity reductions of the Boussinesq equation
• A certain class of solutions of the nonlinear wave equation
• Exact solutions of the multidimensional classical φ6-field equations obtained by symmetry reduction
• Reduction of the representations of the generalised Poincare algebra by the Galilei algebra
• Complex potential equations I. A technique for solution
• Subgroups of the Poincaré group and their invariants

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