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Asymptotic decay of a one-dimensional wave packet in a nonlinear dispersing medium. (Russian) Zbl 0658.35047
The author studies the Cauchy problem for the first order system $\partial u/\partial t+a(u)\partial u/\partial x+b(u)u=0\quad (-\infty <x<\infty,\quad t>0),$ where the unknown function $$u=u(x,t)$$ is searched for by means of the Ansatz $u(x,t,\epsilon)|_{t=0}=\epsilon \sum_{| n| \leq N}\phi_ n(\epsilon x)\exp (inx).$ The purpose of the paper is to describe the asymptotic behaviour of u(x,t,$$\epsilon)$$, as $$\epsilon$$ $$\to 0$$, uniformly for $$x\in {\mathbb{R}}$$ and $$0\leq t\leq O(\epsilon^{-2})$$.
Reviewer: J.Appell

##### MSC:
 35K55 Nonlinear parabolic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35B20 Perturbations in context of PDEs
##### Keywords:
Cauchy problem; first order system; asymptotic behaviour
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