@Article{AAMM-4-6,
author = {Kim, Hongjoong and Moon, Kyoung-Sook},
title = {Stability of Symmetric Solitary Wave Solutions of a Forced Korteweg-de Vries Equation and the Polynomial Chaos},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {6},
pages = {833--847},
abstract = {<p style="text-align: justify;">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 chaos.
The stability studies are focused on the symmetric solitary wave
for the subcritical flow
with the Bond number greater than one third.
When its steady symmetric solitary-wave-like solutions are randomly perturbed,
the evolutions of some waves show stability in time regardless of the randomness
while other waves produce unstable fluctuations.
By representing the perturbation with a random variable,
the governing FKdV equation is interpreted as a stochastic equation.
The polynomial chaos expansion of the random solution has been used
for the study of stability in two ways.
Firstly, it allows us to identify the stable solution of the stochastic governing equation.
Secondly, it is used to construct upper and lower bounding surfaces for unstable solutions,
which encompass the fluctuations of waves.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.12-12S12},
url = {https://global-sci.com/article/73575/stability-of-symmetric-solitary-wave-solutions-of-a-forced-korteweg-de-vries-equation-and-the-polynomial-chaos}
}