Solutions of the system of d'Alembert and eikonal equations, and classification of reductions of PDEs

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Yehorchenko, Irina^1

Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv

01601, Ukraine^1

关键词: d'Alembert equations;    Eikonal equation;    Generalisation;    Independent variables;    Reduction conditions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012018/pdf
DOI  :  10.1088/1742-6596/621/1/012018

来源: IOP

【 摘 要 】

We present an approach to systematic description and classification of solutions of partial differential equations that are obtained by means of reduction of these equations to other equations with smaller number of independent variables. We propose to classify such reductions by means of classification of reduction conditions. The approach is illustrated by an example of the system of d'Alembert and eikonal equations. Solutions of this system were used to outline classification of reductions for the general nonlinear d'Alembert equation, with generalisation to arbitrary Poincaré invariant equations.