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September/October 2009 Solitary waves of the two-dimensional Benjamin equation
Ibtissame Zaiter
Adv. Differential Equations 14(9/10): 835-874 (September/October 2009).

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.

Citation

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Ibtissame Zaiter. "Solitary waves of the two-dimensional Benjamin equation." Adv. Differential Equations 14 (9/10) 835 - 874, September/October 2009.

Information

Published: September/October 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1182.35075
MathSciNet: MR2548280

Subjects:
Primary: 35B40, 35Q53, 74J35

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.14 • No. 9/10 • September/October 2009
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