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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

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
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