On periodic water-waves and their convergence to solitary waves in the long-wave limit
On periodic water-waves and their convergence to solitary waves in the long-wave limit
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DOI：
10.1098/rsta.1981.0231
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发表时间：
1981-12
期刊：
影响因子：
--
通讯作者：
C. Amick;J. Toland
中科院分区：
文献类型：
--
作者：
C. Amick;J. Toland
详细讨论了Nekrasov的方法稳定的水波问题导致一个新的积分方程制定的周期性问题。这一发展使得Amick和Toland（1981）的方法能够适用于长波极限下周期波向孤立波的收敛。此外，它显示了如何经典积分方程制定由于Nekrasov导致，通过最大值原理，新的结果的定性特征的周期波，长期以来一直有一个整体存在的理论（Krasovskii 1961年，Keady & Norbury 1978年）。
A detailed discussion of Nekrasov’s approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of Amick & Toland (1981) to show the convergence of periodic waves to solitary waves in the long-wave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasov leads, via the Maximum Principle, to new results about qualitative features of periodic waves for which there has long been a global existence theory (Krasovskii 1961, Keady & Norbury 1978).