Construction and characterization of solutions converging to solitons for supercritical gKdV equations
Construction and characterization of solutions converging to solitons for supercritical gKdV equations
复制标题
超临界 gKdV 方程收敛到孤子的解的构造和表征
DOI：
--
复制
发表时间：
2009
影响因子：
1.4
通讯作者：
Vianney Combet
中科院分区：
文献类型：
--
作者：
Vianney Combet
我们考虑超临界情形下的广义Korteweg-de弗里斯方程，我们感兴趣的是在H ^1中大时间收敛到孤子的解。在亚临界情况下，变分刻画强迫这种解是精确孤子，但在超临界情况下不存在这样的结果。在本文中，我们首先构造了一个“特殊的解决方案”在这种情况下的紧性参数，即一个解决方案，收敛到一个孤立子，而不是孤立子。其次，利用Pego和Weinstein关于孤立子周围线性化算子谱的描述，构造了一个单参数的特解族，它刻画了所有这些特解.
We consider the generalized Korteweg-de Vries equation in the supercritical case, and we are interested in solutions which converge to a soliton in large time in H^1. In the subcritical case, such solutions are forced to be exactly solitons by variational characterization, but no such result exists in the supercritical case. In this paper, we first construct a "special solution" in this case by a compactness argument, i.e. a solution which converges to a soliton without being a soliton. Secondly, using a description of the spectrum of the linearized operator around a soliton due to Pego and Weinstein, we construct a one parameter family of special solutions which characterizes all such special solutions.