Dissipative waves in a relaxing gas exhibiting mixed nonlinearity

We consider a weakly dissipative quasilinear system of PDEs, governing the unsteady one-dimensional motion of a relaxing gas, and investigate the effects of higher order terms and the source term, present in the differential system, on the wave motion associated with it. The undisturbed state of the medium, which is assumed to be uniform and at rest admits mixed nonlinearity, i.e., the quadratic nonlinearity parameter Gamma inherent in the system changes sign depending on the base state. The method of multiple scales is employed to determine the evolution equation governing small perturbations to the state where Gamma is of O(epsilon), and the effects of nonlinearity are noticeable over times of order O(epsilon(-2))