Spyridon Kamvissis
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On the nonlinear steepest descent method
We will review the history of the nonlinear steepest descent method for the asymptotic evaluation of the solutions of Riemann-Hilbert factorization problems, and then focus on some recent results on the "non-self-adjoint" extension of the theory.
In particular we will consider the case of the semiclassical focusing NLS problem. We will 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 will announce results on existence and regularity of solutions to this variational problem.