The Third‐Order Nonlinear Evolution Equation Governing Wave Propagation in Relaxing Media

Abstract

Initial value problem for the third‐order nonlinear evolution equation governing wave propagation in relaxing media is considered for the case of two space dimensions and small initial data. Existence and uniqueness of the classical solution is established and the solution itself is constructed in the form of a series in the small parameter present in the initial conditions. Long time asymptotic representation is found, which shows that the nonlinearity does not contribute to its major term. The latter consists of two parts corresponding to isotropic and nonisotropic transfer of small perturbations in space.