Wave Processes in Inhomogeneous Nonlinear-Dissipative Media

Several problems for nonlinear localized wave processes are analysed. Wave solutions of the kink type, concentrated in the vicinity of some curve l, are considered. Both the solution and the curve l are unknown. It is shown that the determination of l may be realized without knowledge of the solution. For one class of problems, a variational principle for finding l, similar to the Fermat principle, is obtained. Types of waves are found which exist due to the inhomogeneity of the medium or due to the initial front curvature only.