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A steepest descent method for oscillatory Riemann-Hilbert problems. (English) Zbl 0746.35031

In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, in evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves here exclusively to the modified Korteweg de Vries equation.

MSC:

35Q15 Riemann-Hilbert problems in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
90C99 Mathematical programming
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