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
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. https://doi.org/10.57262/ade/1435064514
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