ABSTRACT
This chapter focuses on a discussion of the nonlinear wave propagation problems which are not governed by the 1 + 1D nonlinear quasi hyperbolic equation, but by more complicated statements. The wave problem in 1 + 2D wave guide, i.e., the longitudinal strain wave propagation in a nonlinearly elastic thin plate will be studied and brought to the explanation of the first experimental observation of the long 2D solitons. The presence of sliding resumes the influence of viscosity and plays a very specific role for solitary wave propagation in a rod embedded into an elastic medium. Stresses on the lateral surface of an elastic wave guide, e.g., an elastic rod, may appear due to its interaction with the surrounding external medium, as in some technological devices. An appearance and evolution of the nonlinear wave in a rod partly embedded in an elastic external medium was studied in numerical simulation.
