Nonlinear traveling waves in a thin layer composed of the Mooney-Rivlin material

In this paper the problem of studies nonlinear traveling waves in the Mooney-Rivlin elastic layer is studied. By averaging the equations of motions over the width of the layer we obtain a system of partial differential equations in one dimensional space and time. A technique of phase planes is used to study the waves processes. Based on the phase trajectory method, we can make an interpretation of conditions of propagation of nonlinear traveling waves and can establish the existence conditions under which the phase plane contains physically acceptable solutions.