Nonlinear Waves. Solitons

Subject of the study. The present article deals with further developing of perturbation method for deformation non-linear waves in an elastic cylinder shell, filled with viscous incompressible liquid, surrounded by an elastic media and under construction damping in longitudial direction. Surrounding medium presence leads to integro-differential equation, to

A set of the nonlinear equations, approximately describing thermoelectrohydrodynamical convection in circular semiconductor cell, which comes to Lorenz model, is obtained. The dependences of the model parameters of materials and ring size, of affixed electric field and of temperature gradient are investigated.

Features of envelope solitons formation in one­dimensional periodic ferromagnetic structure were considered. The model based on the coupled nonlinear Schrodinger equations was used for investigation. The parameter region was calculated in which solitons similar Bragg solitons with different features can arise. Mechanisms of the formation of the solitons localized on the limited length of the structure with different excitation technique were considered.

Investigation results of nonlinear dual-frequency model of resonance transmission line on backward volume magnetostatic waves are demonstrated. The system of two coupled oscillatory circuits is used as a model. The parameters of system depend on the input signal power level and on the detuning value between large and small signals. The results of the model are compared with the experimental data.

Through numerical simulation by nonlinear Schr¨ odinger equation magnetostatic wave soliton formation process is considered when amplitude and shape of initial pulse differ from soliton solution and non-soliton part can influence on soliton evolution. It is shown, that in lossless approximation soliton peak amplitude can oscillate with spatial period L: LD · L · 66 ¢ LD (or friequency W: 0:015 ¢ T¡1 D · W · T¡1 D ), LD и TD – length and time of dispersion.

Principal nonlinear characteristics of transmission lines on the basis of coupled structures with ferromagnetic films at excitation of different types of magnetostatic waves are described proceeding from theoretical and experimental researches. Following types of coupled systems are analyzed: «electrodynamic structure – ferromagnetic film»; the layered structure in the form of two coupled ferromagnetic films, each taken separately is considered as wave controlling structure for magnetostatic waves; and «electrodynamic structure – two coupled ferromagnetic films».