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Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data |
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| Authors: | Jiaqi Liu Peter A Perry Catherine Sulem |
| Institution: | 1. Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, United States;2. Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada |
| Abstract: | The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin. |
| Keywords: | Riemann–Hilbert problem Inverse scattering method Nonlinear steepest descent method |
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