Dynamics of soliton-like wave signals propagating in smoothly inhomogeneous and weakly nonstationary nonlinear media

By employing the nonlinear Klein-Gordon equations with small nonlocal corrections we develop a self-consistent description of one-dimensional soliton-like wave signals in smoothly inhomogeneous nonstationary nonlinear media. For the quasisoliton velocity and the field's integral characteristics we develop a closed system of ordinary differential equations written in a form common in relativistic mechanics. We study the interaction, accompanied by frequency conversion, of quasisolitons with the waves of the medium parameters; in particular, the laws that govern the penetration of these waves into the bulk of an advancing dense-plasma barrier and their reflection from the barrier. Finally, we demonstrate the possibility of the signal frequency growing considerably without temporal-spectrum broadening by employing the example of relativistic quasisolitons propagating in an initially homogeneous and stationary plasma with small additional ionization in the medium