Intermediate systems and invariants

Abstract: In this report some classical and new methods of integration of partial differential equations are considered. The approaches of Monge and Darboux are briefly described. Examples of the construction of general solutions of second order equations based on invariants of the characteristics of hyperbolic equations are given. Intermediate systems of partial derivative equations are introduced in terms of differential algebra. Equations possessing intermediate systems are found.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods