The modified short-wave equation is considered under periodic boundary condition. We prove the global existence of solution with finite energy. We also find traveling wave solutions which is the form of elliptic function.

中文翻译：

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修正的短波方程整体解和行波的存在性

在周期边界条件下考虑了修正的短波方程。我们证明了有限能量解的整体存在性。我们还找到了椭圆函数形式的行波解。