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1996 On the Cauchy problem for the damped Boussinesq equation
Vladimir Varlamov
Differential Integral Equations 9(3): 619-634 (1996). DOI: 10.57262/die/1367969976

Abstract

A classic solution to the Cauchy problem for the damped Boussinesq equation $u_{tt}-2Bu_{txx}=-\alpha u_{xxxx}+u_{xx}-\beta(u^2)_{xx}$, $x\in\Bbb R^1$, $t>0$, $\alpha, B=\text{const}>0$, $\beta=\text{const}\in\Bbb R^1$, with small initial data is constructed by means of the application of both the spectral and perturbation theories. Large time asymptotics of this solution are obtained. Its main term accounts for two solitons traveling in opposite directions. Each of them is governed by the Burgers equation with a transfer.

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Vladimir Varlamov. "On the Cauchy problem for the damped Boussinesq equation." Differential Integral Equations 9 (3) 619 - 634, 1996. https://doi.org/10.57262/die/1367969976

Information

Published: 1996
First available in Project Euclid: 7 May 2013

zbMATH: 0844.35095
MathSciNet: MR1371712
Digital Object Identifier: 10.57262/die/1367969976

Subjects:
Primary: 35Q53

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 3 • 1996
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