метод возмущений

Exact Solitary-wave Solutions of the Burgers – Huxley and Bradley – Harper Equations

Authors: Zemlyanukhin A. I., Bochkarev A. V.

It is shown that the exact soliton-like solutions of nonlinear wave mechanics evolution equations can be obtained by direct perturbation method based on the solution of a linearized equation. The sought solutions are sums of the perturbation series which can be found using the requirement that the series are to be geometric. This requirement leads to the conditions for the coefficients of the equations and parameters of the sought solutions.

The Evolutionary Equation for Wave Processes of the Shift Deformation

Authors: Burenin A. A., Ragozina V. E., Ivanova Y. E.

One-dimensional process of formation and the subsequent motion of a flat cross shock wave is studied on the basis of solutions of the corresponding nonlinear evolutionary equation. This equation defines behaviour of the solution in front area of wave process and follows from interior lines of a method of matched asymptotic expansions. Comparative transient analysis of strains of a deformation and volume will be carried out and their basic differences are specified.