Advances in Differential Equations

Solitary waves of the two-dimensional Benjamin equation

Ibtissame Zaiter

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

In this paper, we study the existence of solitary waves associated to the two-dimensional Benjamin equation. This equation governs the evolution of waves at the interface of a two-fluid system in which surface-tension effects cannot be ignored. We classify the existence and nonexistence cases according to the sign of the transverse dispersion coefficients. Moreover, we show that the solitary waves of the 2D Benjamin equation, when they exist, converge to those of the KPI equation as the parameter preceding the nonlocal operator $H\partial^2_x$ goes to zero. We also prove the regularity of solitary waves, as well as their symmetry with respect to the transverse variable and their algebraic decay at infinity.

Article information

Source
Adv. Differential Equations Volume 14, Number 9/10 (2009), 835-874.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355863332

Mathematical Reviews number (MathSciNet)
MR2548280

Zentralblatt MATH identifier
1182.35075

Subjects
Primary: 35B40: Asymptotic behavior of solutions 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 74J35: Solitary waves

Citation

Zaiter, Ibtissame. Solitary waves of the two-dimensional Benjamin equation. Adv. Differential Equations 14 (2009), no. 9/10, 835--874. https://projecteuclid.org/euclid.ade/1355863332.


Export citation