Nonexistence of small, odd breathers for a class of nonlinear wave equations
Nonexistence of small, odd breathers for a class of nonlinear wave equations
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DOI：
10.1007/s11005-016-0930-y
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发表时间：
2016-07
影响因子：
1.2
通讯作者：
M. Kowalczyk;Y. Martel;Claudio Muñoz
中科院分区：
文献类型：
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作者：
M. Kowalczyk;Y. Martel;Claudio Muñoz
在这篇注记中，我们证明了对于一大类具有奇非线性的非线性波动方程，任何在能量空间中很小的整体定义的奇解在局部能量范数中衰减到0。特别地，这一结果显示了一些经典的非线性Klein Gordon方程，如Sine-Gordon方程和模型，不存在小的、奇异的呼吸子。它还部分地回答了Soffe和Weinstein(发明数学136(1)：9-74，第19页1999)关于一维立方NLKG不存在呼吸子的问题。
In this note, we show that for a large class of nonlinear wave equations withoddnonlinearities, any globally defined odd solution which is small in the energy space decays to 0 in the local energy norm. In particular, this result shows nonexistence of small, odd breathers for some classical nonlinear Klein Gordon equations, such as the sine-Gordon equation andandmodels. It also partially answers a question of Soffer and Weinstein (Invent Math 136(1): 9–74, p 19 1999) about nonexistence of breathers for the cubic NLKG in dimension one.