Differential and Integral Equations

On the Cauchy problem for the damped Boussinesq equation

Vladimir Varlamov

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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

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

First available in Project Euclid: 7 May 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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