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September/October 2015 Stability and decay properties of solitary-wave solutions to the generalized BO--ZK equation
Jerry L. Bona, Amin Esfahani, Ademir Pastor
Adv. Differential Equations 20(9/10): 801-834 (September/October 2015).

Abstract

Studied here is the generalized Benjamin-Ono--Zakharov-Kuznetsov equation $$ u_t+u^pu_x+\alpha\mathscr{H}u_{xx}+\varepsilon u_{xyy}=0, \quad (x,y)\in \mathbb R ^2,\;\;t\in \mathbb R ^+, $$ in two space dimensions. Here, $\mathscr{H}$ is the Hilbert transform and subscripts denote partial differentiation. We classify when this equation possesses solitary-wave solutions in terms of the signs of the constants $\alpha$ and $\varepsilon$ appearing in the dispersive terms and the strength of the nonlinearity. Regularity and decay properties of these solitary wave are determined and their stability is studied.

Citation

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Jerry L. Bona. Amin Esfahani. Ademir Pastor. "Stability and decay properties of solitary-wave solutions to the generalized BO--ZK equation." Adv. Differential Equations 20 (9/10) 801 - 834, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1325.35162
MathSciNet: MR3360392

Subjects:
Primary: 35A15, 35B35, 35B40, 35Q35, 35Q51

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.20 • No. 9/10 • September/October 2015
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