On periodic waves for sine- and sinh-Gordon equations
On periodic waves for sine- and sinh-Gordon equations
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DOI：
10.1016/j.jmaa.2011.01.020
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发表时间：
2011-07
影响因子：
1.3
通讯作者：
F. Natali
中科院分区：
文献类型：
--
作者：
F. Natali
本文将讨论与正弦戈登方程和辛-戈登方程相关的周期波的存在性和轨道稳定性/不稳定性的结果。已知正弦戈登方程是完全可积的，精确可解的，它有几个特殊的解，如孤子解和呼吸解。在这两种情况下，我们都得到了一个周期变符号波，它在整条实线上是光滑的。使用的主要工具是格里拉基斯、沙塔和施特劳斯的理论。
Results of existence as well as orbital stability/instability of periodic waves associated with sine-Gordon and sinh-Gordon equations will be treated in this manuscript. The sine-Gordon equation is known to be completely integrable, exactly solvable and it has several special solutions as soliton and breather solutions. We obtain in both cases, a periodic sign-changed wave which is smooth when posed on whole real line. The main tool used is the Grillakis, Shatah and Straussʼ theory.