Dissipative Waves in a Relaxing Gas Exhibiting Mixed Nonlinearity

We consider a weakly dissipative quasilinear system of PDEs, governingthe unsteady one-dimensional motion of a relaxing gas, and investigatethe effects ofhigher order terms and the source term, present in the differentialsystem, on the wave motion associated with it. The undisturbed stateof the medium, which is assumed to be uniform and at restadmits mixed nonlinearity, i.e., the quadratic nonlinearity parameter inherent in the system changes sign depending on the basestate. The method of multiple scales is employed to determine theevolution equation governing small perturbations to the state where is of O(), and the effects of nonlinearity arenoticeable over times of order O(^–2).