Reduction of non-linear d'Alembert equations to two-dimensional equations

Abstract

We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the reduced equations represent interesting classes of two-dimensional parabolic, hyperbolic and elliptic equations. Ansatzes and methods used for reduction of the d'Alembert (n-dimensional wave) equation can be also used for arbitrary Poincare-invariant equations. This seemingly simple and partial problem involves many important aspects in the studies of the PDE.

The published paper with some mistakes corrected

References in corpus (2)

• Applications of Symmetry Methods to the Theory of Plasma Physics
• On reduction of multi-dimensional non-linear wave equation to two-dimensional equations

Cited by in corpus (1)

• Reduction of Multidimensional Wave Equations to Two-Dimensional Equations: Investigation of Possible Reduced Equations