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Nonlinear wave motion governed by the modified Burgers equation. (English) Zbl 0643.35091
The modified Burgers equation \[ \partial V/\partial x+V^ 2(\partial V/\partial t)=\epsilon (\partial^ 2V/\partial t^ 2),\quad \epsilon >0 \] is considered. The authors’ aim is to find asymptotic solutions to that equation for small values of the coefficient, but all values of (x,t). The results are achieved by systematic use of matched asymptotic expansion techniques.
Furthermore, the authors study certain specific initial distributions and analyze some shock solutions.
Reviewer: N.Jacob

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35G20 Nonlinear higher-order PDEs
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
35C20 Asymptotic expansions of solutions to PDEs
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