Similarities and exact solutions of transonic gas flow model

Abstract

In this work, one of the important models in nonlinear wave theory and also in nonlinear acoustic, the Lin–Reissner–Tsien (LRT) equation is considered. For the homogeneous form of LRT equation, the exact solutions are obtained. For steady and non-steady state forms of the LRT equation with force terms, similarity reductions are obtained via the classical symmetry analysis method. Both of the considered problems are not seen in the literature. The results obtained in this paper are new solutions and believed to have a major role in the development of the model.