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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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

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

First available in Project Euclid: 23 June 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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