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arXiv · 0909.2020

Stability and Decay properties of Solitary wave solutions for the generalized BO-ZK equation

Amin Esfahani·Ademir Pastor·Jerry L. Bona
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Abstract

Studied here is the generalized Benjamin-Ono--Zakharov-Kuznetsov equation $u_t+u^pu_x+\alpha\mathscr{H}u_{xx}+\varepsilon u_{xyy}=0, \quad (x,y)\in\rr^2\!,\;\;t\in \rr^+\!$ in two space dimensions. Here, $\mathscr{H}$ is the Hilbert transform and subscripts denote partial differentiation. We classify when equation (1) 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.

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Amin Esfahani, Ademir Pastor, Jerry L. Bona. 2009-09-10. Stability and Decay properties of Solitary wave solutions for the generalized BO-ZK equation. https://arxiv.org/abs/0909.2020

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