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From Stationary Phase to Steepest Descent

Spyridon Kamvissis
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Abstract

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 Schrödinger 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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Spyridon Kamvissis. 2008-03-04. From Stationary Phase to Steepest Descent. https://arxiv.org/abs/math-ph/0701033

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