Advances in Differential Equations

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

Jerry L. Bona and Yue Liu

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35R25: Improperly posed problems 37K40: Soliton theory, asymptotic behavior of solutions 37N10: Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10] 76B25: Solitary waves [See also 35C11] 76E30: Nonlinear effects

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.


Export citation