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From Stationary Phase to Steepest Descent

Mathematical Physics 2008-12-01 v5 math.MP

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 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.

Keywords

Cite

@article{arxiv.math-ph/0701033,
  title  = {From Stationary Phase to Steepest Descent},
  author = {Spyridon Kamvissis},
  journal= {arXiv preprint arXiv:math-ph/0701033},
  year   = {2008}
}

Comments

Dedicated to Percy Deift on his 60th birthday