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Integral convergence of the higher-order theory for solitary waves

Wang, Xinlong and Wu, Theodore Yaotsu (2006) Integral convergence of the higher-order theory for solitary waves. Physics Letters A, 350 (1-2). pp. 44-50. ISSN 0375-9601. doi:10.1016/j.physleta.2005.10.006.

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An exact analytic solution for a solitary wave of arbitrary height is attained by series expansions of flow variables based on parameter ε = k²h², (k being the wave number of the solitary wave on water of uniform depth h) by orders in O(ε^n) up to n = 25. Its convergence behavior is found first to yield a set of asymptotic representations for all the flow variables, each and every becoming highest in accuracy at O(ε^(17). For n > 17, the field variables and wave parameters, e.g., wave amplitude, have their errors continue increasing with n, but, in sharp contrast, all the wave integral properties including the excess mass first undergo finite fluctuations from O(ε^(17) to O(ε^(20), then all converge uniformly beyond in a group of tight bundle within the range 0 < ε < 0.283, with ε = 0.283 corresponding to the highest solitary wave with a 120° vertex angle. This remarkable behavior of series convergence seems to have no precedent, and furthermore, is unique in ε, not shared by the exact solutions based on all other parameters examined here.

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Additional Information:© 2005 Elsevier. Received 20 February 2005, Revised 30 August 2005, Accepted 4 October 2005, Available online 10 October 2005. The work of Xinlong Wang is supported by the National Science Foundation of China under Grant No. 19925414, 10474045, the Special Funds for Major State Basic Research Projects of China under Grant No. G2000077302, and the Huaying Foundation of Education & Culture. We are deeply appreciative for the encouraging sponsorship by the American–Chinese Scholarship Foundation.
Funding AgencyGrant Number
National Natural Science Foundation of China19925414
National Natural Science Foundation of China10474045
Special Funds for Major State Basic Research Projects of ChinaG2000077302
Huaying Foundation of Education and CultureUNSPECIFIED
American-Chinese Scholarship FoundationUNSPECIFIED
Subject Keywords:Surface solitary-wave; High-order solution; Convergence of series solution
Issue or Number:1-2
Record Number:CaltechAUTHORS:20200306-150642521
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Official Citation:Xinlong Wang, Theodore Yaotsu Wu, Integral convergence of the higher-order theory for solitary waves, Physics Letters A, Volume 350, Issues 1–2, 2006, Pages 44-50, ISSN 0375-9601,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101759
Deposited By: George Porter
Deposited On:06 Mar 2020 23:29
Last Modified:16 Nov 2021 18:05

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