Abstract

About Some Class of the Invariant Solutions of Partial Differential Equations Set

A.Kusyumov (Aerodynamics Department, Kazan State Technical University, Kazan, Russia)

e-mail: postbox7@mail.ru

It is known that the partial differential equations set symmetries are allowed to facilitate an integration of the set. In particular, it is possible to obtain a factor - system with smaller dimension of independent variables space. It is known also that the symmetries are allowed to obtain a parametric representation of the solutions of ordinary differential equations set. In the present paper the method of using of partial differential equations set symmetries for construction of the solution, defined a vector field integral curve on integral manifold of the equations set is considered. Such solutions as the one-parameter solutions along the vector field are called. The given class of the solutions can be defined proceeding from geometrical interpretation of an invariance condition as conditions of the vector field tangency of a surface, defined the initial equations set. Thus it is taken into account, that the vector field tangents not only considered surface, but also own integral curve. The possibility of the one-parameter solutions along a vector field using for an integration of partial differential equations set with arbitrary boundary conditions is considered.

Section : 12