Method of the exterior differential forms and problem of the
conservation laws determination for partial differential equations system
A.N.Kusyumov
KSTU, Russia
There are
different techniques of a conservation laws determination for arbitrary partial
differential equations systems. We can use the Euler-Langrange operator or
operator of an universal linearization. In this paper the technique
transformation of the partial differential equations system to a system of the
exterior differential equations is considered. This technique also may be used
for determination of the conservation laws of arbitrary equations system. The
exterior differential forms were used by A.M.Vasil’ev for the conservation laws
determination. The closure of some differential 2-form was used by him as a
condition of existence of conservation laws for a partial differential
equations system with two independent variables. Here we use modified approach.
The condition of some set 1-forms closure is used as the condition of
conservation laws existence. Some problems of this method were considered also
in our other papers.