New traveling wave rational form exact solutions for strain wave equation in micro structured solids

Abstract

Strain wave equation is a fourth order non-linear partial differential equation that arises in the study of non-dissipative strain wave propagation in micro structured solids. This equation also represents the dynamics of several physical phenomena. This equation can also be consider as a generalization of Boussinesq equation with dual dispersion. In this paper, a general strain wave equation is considered and obtained several new exact solutions. A variant of F-expansion method is applied to obtain the required solutions. The available traveling wave exact solutions are primarily obtained by integrating the resulting fourth order ordinary differential equation twice. But, in this paper, we show that there exist several traveling wave solutions to strain wave equation which cannot be derived using the existing methods. Several families of new exact solutions in rational function form are derived using this novel method, without performing the initial integration.