Symmetry and decay of traveling wave solutions to the Whitham equation

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• 作者：Gabriele Bruell ; ^{gabriele.bruell@math.ntnu.no} ; Mats Ehrnstr&ouml ; m ^{mats.ehrnstrom@math.ntnu.no} ; Long Pei ^{long.pei@math.ntnu.no}
• 关键词：35Q53 ; 35B06 ; 35B40 ; 35S30 ; 45K05
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：262
• 期：8
• 页码：4232-4254
• 全文大小：363 K
• 卷排序：262

文摘

This paper is concerned with decay and symmetry properties of solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is shown that all such solitary-wave solutions are symmetric and monotone on either side of the crest. The proof is based on the method of moving planes. Furthermore, a close relation between symmetric and traveling-wave solutions is established.