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A steepest descent method for oscillatory Riemann–Hilbert problems: asymptotics for the MKdV equation
 Ann. of Math
, 1993
"... In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory RiemannHilbert problems. Such problems arise, in particular, in evaluating the longtime behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves ..."
Abstract

Cited by 303 (27 self)
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here exclusively to the modified Korteweg de Vries (MKdV) equation, yt − 6y 2 yx + yxxx = 0, − ∞ < x < ∞, t ≥ 0, y(x, t = 0) = y0(x), but it will be clear immediately to the reader with some experience in the field, that the method extends naturally and easily to the general class of wave
A Random Field Model and its Application in Industrial Production.
"... Let X be an abstract set. We consider a prior random field Yx = U + VWx, where U is a real random variable following a uniform distribution on an interval [−m,m], where V is a real and positive random variable following a uniform distribution on an interval [, 1/] and where (Wx)x∈X is a centered nor ..."
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. Denote Σ: = (k (xi, xj))1≤i,j≤n the matrix of correlations and k (x): = (k (x, xj))1≤j≤n the correlation vector. We suppose that we are in a generic position so that the matrix Σ is invertible. Theorem 3. The conditional distribution of the random field (Yx)x∈X knowing that (Yxi = yi)1≤i≤n is given