Stability and decay properties of solitary-wave solutions to the generalized BO--ZK equation
Stability and decay properties of solitary-wave solutions to the generalized BO--ZK equation
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广义BO--ZK方程孤波解的稳定性和衰减特性
DOI：
10.57262/ade/1435064514
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发表时间：
2009
影响因子：
1.4
通讯作者：
J. Bona
中科院分区：
文献类型：
--
作者：
A. Esfahani;A. Pastor;J. Bona
研究了二维空间中的广义本杰明-奥诺-扎哈罗夫-库兹涅佐夫方程$u_t+u^pu_x+\alpha\mathscr{H}u_{xx}+\varepsilon uxy=0，quad(x，y).这里，$\mathscr{H}$是希尔伯特变换，下标表示偏微分。对于方程(1)何时有孤立波解，我们根据出现在色散项中的常数α和α的符号和非线性的强度来进行分类。确定了这些孤立波的正则性和衰减性，并研究了它们的稳定性。
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.