Preprint 13/2005

On the Method of Steepest Descent

Spyridon Kamvissis

Contact the author: Please use for correspondence this email.
Submission date: 20. Feb. 2005 (revised version: February 2005)
Pages: 28
Bibtex
Keywords and phrases: steepest descent, riemann-hilbert factorization
Download full preprint: PDF (254 kB), PS ziped (192 kB)

Abstract:
We review the history of the nonlinear steepest descent method for the asymptotic evaluation of the solutions of Riemann-Hilbert factorization problems. We stress some recent results on the "non-self-adjoint" extension of the theory. In particular we consider the case of the semiclassical focusing NLS problem. We explain how the nonlinear steepest descent method gives rise to a maximin variational problem for Green potentials with external field in two dimensions and we announce results on existence and regularity of solutions to this variational problem.

07.06.2018, 02:11