Modified Energy Functionals and the NLS Approximation
Modified Energy Functionals and the NLS Approximation
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DOI：
10.3934/dcds.2017054
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发表时间：
2016-05
期刊：
影响因子：
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通讯作者：
P. Cummings;C. E. Wayne
中科院分区：
文献类型：
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作者：
P. Cummings;C. E. Wayne
我们考虑[14]中的一个模型方程，它捕捉了水波方程的重要性质。给出了该方程的波包解可用非线性薛定谔方程近似的新证明。这一证明简化并加强了[14]的结果，使得近似NLS解的存在性在整个区间而不仅仅是一个子区间上都成立。此外，该证明通过使用由[1]和[8]激发的修改的能量泛函来避免与[14]中的范式变换的逆相关联的问题。
We consider a model equation from [14] that captures important properties of the water wave equation. We give a new proof of the fact that wave packet solutions of this equation are approximated by the nonlinear Schrodinger equation. This proof both simplifies and strengthens the results of [14] so that the approximation holds for the full interval of existence of the approximate NLS solution rather than just a subinterval. Furthermore, the proof avoids the problems associated with inverting the normal form transform in [14] by working with a modified energy functional motivated by [1] and [8].