Stability of symmetric solitarywave solutions of a forced korteweg-de vries equation and the polynomial Chaos

Hongjoong Kim, Kyoung Sook Moon

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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 solitarywave- 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. First 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.

Original languageEnglish
Pages (from-to)833-847
Number of pages15
JournalAdvances in Applied Mathematics and Mechanics
Volume4
Issue number6
DOIs
Publication statusPublished - 2012 Dec 1

Fingerprint

Korteweg-de Vries equation
Polynomial Chaos
Solitary Wave Solution
Korteweg-de Vries Equation
Chaos theory
Polynomials
Stochastic Equations
Unstable
Capillary-gravity Waves
Fluctuations
Chaos Expansion
Stable Solution
Numerical Stability
Solitary Waves
Randomness
Governing equation
Convergence of numerical methods
Random variable
Solitons
Random variables

Keywords

  • Forced Korteweg-de Vries equation
  • Polynomial chaos
  • Solitary waves
  • Stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Mechanical Engineering

Cite this

Stability of symmetric solitarywave solutions of a forced korteweg-de vries equation and the polynomial Chaos. / Kim, Hongjoong; Moon, Kyoung Sook.

In: Advances in Applied Mathematics and Mechanics, Vol. 4, No. 6, 01.12.2012, p. 833-847.

Research output: Contribution to journalArticle

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