International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Ibragimov N.H.   Meleshko S.V.   Rudenko O.V.  

Group properties of evolutionary integro-differential equation

Reporter: Meleshko S.V.

The presentation deals with a evolutionary integro-differential equation describing nonlinear waves. Particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since solutions of these equations describe many physical phenomena, analysis of the studied in the paper equation is important. One of the methods for obtaining solutions is the group analysis method. Since the equation is integro-differential, the classical group analysis method cannot be applied. Discussion of some approaches of modern group analysis to the equation is considered in the presentation.