| Abstract: | A method of constructing asymptotic approximations of wide classes of solutions of weakly non-linear systems is proposed based on the averaging scheme developed in /1–3/.****See also: Krylov A.V. and Shtaras A.L. Internal averaging of multidimensional weakly non-linear systems along characteristics, Dep. in LitNIINTI, 10.11.86, No.1750, 1986). The method enables one to obtain the conditions for the asymptotic decay of systems described by the Burgers, Korteweg-de Vries and similar scalar equations, and also enables one to investigate problems in which this decay does not occur. As an example we investigate the propagation of perturbations in an elastic non-uniform tube. The interaction between two waves is considered and the conditions for resonance are obtained. |
