Asymptotic solutions and conservation laws for the nonlinear Schrödinger equation. I
- 1 May 1976
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 17 (5) , 710-713
- https://doi.org/10.1063/1.522967
Abstract
In the absence of solitons, the nonlinear Schrödinger equation has an asymptotic solution which decays in time as t−1/2, and contains two arbitrary functions (in the amplitude and phase, respectively). For appropriate initial data, the amplitude function is uniquely determined in terms of the initial data by the conservation laws; the other function is undetermined. This method determines the leading two terms in each of the asymptotic expansions for the amplitude and phase, but no more. The method makes no direct use of th Marchenko integral equations.Keywords
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