Differential and Integral Equations

On the Cauchy problem for the damped Boussinesq equation

Vladimir Varlamov

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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.

Article information

Source
Differential Integral Equations, Volume 9, Number 3 (1996), 619-634.

Dates
First available in Project Euclid: 7 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367969976

Mathematical Reviews number (MathSciNet)
MR1371712

Zentralblatt MATH identifier
0844.35095

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Citation

Varlamov, Vladimir. On the Cauchy problem for the damped Boussinesq equation. Differential Integral Equations 9 (1996), no. 3, 619--634. https://projecteuclid.org/euclid.die/1367969976


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