Stability of Symmetric Solitary Wave Solutions of a Forced Korteweg-de Vries Equation and the Polynomial Chaos
作者机构：Department of MathematicsKorea UniversitySeoul 136-701Korea Mathematics&InformationGachon UniversityGyeonggi-do 461-701Korea
出 版 物：《Advances in Applied Mathematics and Mechanics》 (应用数学与力学进展（英文）)
年 卷 期：2012年第4卷第6期
页 面：833-847页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：The authors are grateful to the anonymous referees for their valuable comments and suggestions.This research of Kim was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education Science and Technology(20110005272)
主 题：Stability solitary waves polynomial chaos forced Korteweg-de Vries equation
摘 要：In this paper,we consider the numerical stability of gravity-capillary waves generated by a localized pressure in water of finite depth based on the forced Korteweg-de Vries(FKdV)framework and the polynomial *** stability studies are focused on the symmetric solitary wave for the subcritical flow with the Bond number greater than one *** its steady symmetric solitarywave-like solutions are randomly perturbed,the evolutions of some waves show stability in time regardless of the randomness while other waves produce unstable *** representing the perturbation with a random variable,the governing FKdV equation is interpreted as a stochastic *** polynomial chaos expansion of the random solution has been used for the study of stability in two *** it allows us to identify the stable solution of the stochastic governing *** it is used to construct upper and lower bounding surfaces for unstable solutions,which encompass the fluctuations of waves.
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