Abstract

A New Method of Separation of Variables for Certain Linear Problems of Mathematical Physics

A.Shanin (Department of Acoustics, Faculty of Physics, Moscow State University, Moscow, Russia)

e-mail: shanin@ort.ru

It is well known that the traditional procedure of separation of variables is deeply connected with the invariance of the differential operator with respect to a symmetry operator. This enables one to decribe all admissible coordinate systems for each equation. Unfortunately, many interesting problems do not admit the separation of variables. Here we describe the method to transform the PDE boundary problem into the system of ODEs. This method can be treated as a generalization of the separation of variables. The method can be applied to a wide class of problems; it is based on the group invariance and the theorem of the uniqueness for the initial PDE problem.

Section : 12