In this paper, we are concerned with the Cauchy problem for a generalized two-component Dullin–Gottwald–Holm system arising from the shallow water regime with nonzero constant vorticity. We provide new sufficient conditions on the initial data which lead to the local-in-space blow-up. In addition, it is shown that horizontally symmetric weak solutions to this system must be traveling wave solutions.

中文翻译：

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广义两分量Dullin-Gottwald-Holm系统的空间局部爆破和行波解的对称性

在本文中，我们关注由具有非零恒定涡度的浅水区域引起的广义两分量Dullin-Gottwald-Holm系统的柯西问题。我们为初始数据提供了新的充分条件，这会导致空间爆炸。另外，表明该系统的水平对称弱解必须是行波解。