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

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

Duke Scholars

Author Stephanos Venakides Mathematics