Advances in Differential Equations

Stability and decay properties of solitary-wave solutions to the generalized BO--ZK equation

Jerry L. Bona, Amin Esfahani, and Ademir Pastor

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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.

Article information

Source
Adv. Differential Equations Volume 20, Number 9/10 (2015), 801-834.

Dates
First available in Project Euclid: 23 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.ade/1435064514

Mathematical Reviews number (MathSciNet)
MR3360392

Zentralblatt MATH identifier
1325.35162

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics 35B40: Asymptotic behavior of solutions 35B35: Stability 35Q51: Soliton-like equations [See also 37K40] 35A15: Variational methods

Citation

Esfahani, Amin; Pastor, Ademir; Bona, Jerry L. Stability and decay properties of solitary-wave solutions to the generalized BO--ZK equation. Adv. Differential Equations 20 (2015), no. 9/10, 801--834. https://projecteuclid.org/euclid.ade/1435064514.


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