The dynamics of nonlinear wave beam with variable nonlinearity

Studies of the dynamics of nonlinear wave beams in inhomogeneous media with continuously variable non-linearity and phase distortions in the initial data led us to the conclusion that the dominant contribution to the nonlinearity of the variable generation of new resonance wave structures. At the same time we studied how the quantization of the waves and the birth of the continuous spectrum.

The purpose of this work was to study the problem of generation and propagation of nonlinear wave beams in nonlinear dynamic environment. This paper discusses the problem with emphasis on physically significant effects in the problem of generation, generated primarily by changing nonlinearity coefficient along the propagation path. Studies have shown that for sufficiently smooth (adiabatic) change the nonlinearity coefficient of the beam structure is maintained, or soliton-soliton solutions retain their structure to change the width and amplitude of the beam energy conservation.

At the same time it was found that the sudden change of the nonlinearity coefficient chand the solution character and the «quantization rule» stimulates the transformation of one-soliton and multi-soliton solutions with each other. If you violate the «quantization rule», a part of the energy is displayed. In addition it is shown that an increase in the coefficient of non-linearity in the presence of the wave fields in the vicinity of the soliton leads to a significant increase in the amplitude of the solitary wave, actually leading to the formation of «waves-killers».