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435
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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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
A nonlinear stationary phase method for oscillatory RiemannHilbert problems
 Int. Math. Res. Not. IMRN
"... ar ..."
Renormalization in quantum field theory and the RiemannHilbert problem. II. The βfunction, diffeomorphisms and the renormalization group
 Comm. Math. Phys
"... We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given by evalu ..."
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Cited by 332 (39 self)
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We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given
Nonoscillatory central differencing for hyperbolic conservation laws
 J. COMPUT. PHYS
, 1990
"... Many of the recently developed highresolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the fieldbyfield decomposition which is required in orde ..."
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Cited by 298 (25 self)
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in order to identify the “direction of the wind. ” Instead, we propose to use as a building block the more robust LaxFriedrichs (LxF) solver. The main advantage is simplicity: no Riemann problems are solved and hence fieldbyfield decompositions are avoided. The main disadvantage is the excessive
Semiclassical asymptotics of orthogonal polynomials, RiemannHilbert problem, and universality in the matrix model
, 1999
"... We derive semiclassical asymptotics for the orthogonal polynomials Pn(z) on the line with respect to the exponential weight exp(−NV (z)), where V (z) is a doublewell quartic polynomial, in the limit when n,N → ∞. We assume that ε ≤ (n/N) ≤ λcr − ε for some ε> 0, where λcr is the critical value ..."
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Cited by 166 (11 self)
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of the ratio n/N. The proof of the semiclassical asymptotics is based on the methods of the theory of integrable systems and on the analysis of the appropriate matrix RiemannHilbert problem. As an application of the semiclassical asymptotics of the orthogonal polynomials, we prove the universality
ON THE RIEMANNHILBERT PROBLEMS
, 1998
"... We discuss some topological aspects of the RiemannHilbert transmission problem and RiemannHilbert monodromy problem on Riemann surfaces. In particular, we describe the construction of a holomorphic vector bundle starting from the given representation of the fundamental group and investigate the lo ..."
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We discuss some topological aspects of the RiemannHilbert transmission problem and RiemannHilbert monodromy problem on Riemann surfaces. In particular, we describe the construction of a holomorphic vector bundle starting from the given representation of the fundamental group and investigate
Results 1  10
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435