Numerical simulations of the stochastic KDV equation

UNCW Author/Contributor (non-UNCW co-authors, if there are any, appear on document)
Andrew Rose (Creator)
Institution
The University of North Carolina Wilmington (UNCW )
Web Site: http://library.uncw.edu/
Advisor
Russell Herman

Abstract: We study the Korteweg-de Vries (KdV) equation with external noise and compare our numerical simulations to known theoretical results. By using a modification of the Zabusky-Kruskal finite difference scheme, we are able to generate numerical solutions to the stochastic KdV. We look at the large time behavior of the stochastic KdV and verify the diffusion of solitons. We find that the predicted large time behavior of the perturbed solution is not easily confirmed in the simulations as the initial soliton diffuses and is lost amidst the background noise long before the asymptotic limit is reached.

Additional Information

Publication
Thesis
A Thesis Submitted to the University of North Carolina at Wilmington in Partial Fulfillment of the Requirement for the Degree of Masters of Science
Language: English
Date: 2009
Keywords
Boundary value problems, Korteweg-de Vries equation, Perturbation (Mathematics)
Subjects
Boundary value problems
Perturbation (Mathematics)
Korteweg-de Vries equation