From Stationary Phase to Steepest Descent

Details From Stationary Phase to Steepest Descent From Stationary Phase to Steepest Descent

2007-01-11

arxiv.org/abs/math-ph/0701033v5

Contemporary Mathematics, v.458, AMS 2008, pp.145-162.

Physics

Mathematical Physics

Dedicated to Percy Deift on his 60th birthday

Scientific paper

Our aim here is to clarify the distinction between the nonlinear-stationary-phase idea and the nonlinear-steepest-descent idea, stressing the importance of actual steepest-descent contours in some problems. We mostly use the nonlinear Schr\"odinger equation as our working model, but we also digress to the KdV equation at some point. This is a slightly revised version of a review paper that will appear in the forthcoming volume (Contemporary Mathematics, AMS) honoring Percy Deift.

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