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