## Differential and Integral Equations

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

### On the Cauchy problem for the damped Boussinesq equation

#### 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