Publications [#320452] of Stephanos Venakides

Papers Published

1. Venakides, S, The zero dispersion limit of the korteweg‐de vries equation for initial potentials with non‐trivial reflection coefficient, Communications on Pure and Applied Mathematics, vol. 38 no. 2 (January, 1985), pp. 125-155, WILEY [doi]
   (last updated on 2026/01/13)

   Abstract:
   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