二维Benjamin-Ono方程孤波解的存在性与分析
On the existence and analycity of solitary waves solutions to a two-dimesional Benjamin-Ono equation
摘要：
我们证明了与下列方程\begin{eqnarray*} (u_t+u^{p}u_x+ \mathcal H\partial_x^2u+ λ\mathcal H\partial_y^2u)_x +μu_{yy}=0, \end{eqnarray*}相关的孤波的存在性、正则性和解析性，其中$\mathcal H$是关于$x$的希尔伯特变换，并且$λ$和$μ$是非负实数，不同时为零.
英文摘要：
We show the existence, regularity and analyticity of solitary waves associated to the following equation \begin{eqnarray*} (u_t+u^{p}u_x+ \mathcal H\partial_x^2u+ λ\mathcal H\partial_y^2u)_x +μu_{yy}=0, \end{eqnarray*} where $\mathcal H$ is the Hilbert transform with respect to $x$ and $λ$ and $μ$ are nonnegative real numbers, not simultaneously zero.
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