The zero dispersion limit of the korteweg‐de vries equation for initial potentials with non‐trivial reflection coefficient

Published

Journal Article

The inverse scattering method is used to determine the distribution limit as ϵ → 0 of the solution u(x, t, ϵ) of the initial value problem. Ut − 6uux + ϵ2uxxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The case v(x) ≪ 0 has been solved by Peter D. Lax and C. David Levermore [8], [9], [10]. The computation of the distribution limit of u(x, t, ϵ) as ϵ → 0 is reduced to a quadratic maximization problem, which is then solved. Copyright © 1985 Wiley Periodicals, Inc., A Wiley Company

Full Text

Duke Authors

Cited Authors

  • Venakides, S

Published Date

  • January 1, 1985

Published In

Volume / Issue

  • 38 / 2

Start / End Page

  • 125 - 155

Electronic International Standard Serial Number (EISSN)

  • 1097-0312

International Standard Serial Number (ISSN)

  • 0010-3640

Digital Object Identifier (DOI)

  • 10.1002/cpa.3160380202

Citation Source

  • Scopus