## Advances in Differential Equations

### Instability of solitary-wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation

#### Abstract

The generalized Kadomtsev-Petviashvili system of equations in three space dimensions, $$\begin{cases} u_t + u^p u_x + u_{xxx} - v_y - w_z = 0, \\ v_x = u_y, \\ w_x = u_z, \end{cases} \tag*{(*)}$$ has been shown by de Bouard and Saut to possess solitary-wave solutions if and only if $1 \le < 4/3.$ It is demonstrated here that these localized traveling-waves, when considered as solutions of the initial-value problem for $(*)$, are dynamically unstable to perturbations.

#### Article information

Source
Adv. Differential Equations Volume 7, Number 1 (2002), 1-23.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651873

Mathematical Reviews number (MathSciNet)
MR1867702

Zentralblatt MATH identifier
1223.35271

#### Citation

Bona, Jerry L.; Liu, Yue. Instability of solitary-wave solutions of the 3-dimensional Kadomtsev-Petviashvili equation. Adv. Differential Equations 7 (2002), no. 1, 1--23. https://projecteuclid.org/euclid.ade/1356651873.