MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

On the Method of Steepest Descent

Spyridon Kamvissis


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.

Feb 20, 2005
Feb 20, 2005
steepest descent, riemann-hilbert factorization

Related publications

2005 Repository Open Access
Spyridon Kamvissis

On the method of steepest descent