Exact solutions of gasdynamic equations obtained by the method of conservation laws

In the present paper, the recent method of conservation laws for constructing exact solutions for systems of nonlinear partial differential equations is applied to the gasdynamic equations describing one-dimensional and three-dimensional polytropic flows. In the one-dimensional case singular solutions are constructed in closed forms. In the three-dimensional case several conservation laws are used simultaneously. It is shown that the method of conservation laws leads to particular solutions different from group invariant solutions.

► Method of conservation laws is applied to gasdynamic equations.
► Exact solutions are constructed in implicit form using mass conservation.
► Singular solutions are presented in closed forms.
► Constructed solutions are different from group invariant solutions.
► More exact solutions can be found using other conservation laws.