The matrix Riemann-Hilbert factorization approach is used to derive the leading-order, exponentially small asymptotics as t --\* +oo such that x/t ~ O(1) of solutions to the Cauchy problem for the defocusing nonlinear Schr6dinger equation, iOtu + 02xu -2([ul 2 -1)u = 0, with finite density initial d
✦ LIBER ✦
Sharp Lr asymptotics of the small solutions to the nonlinear Schrödinger equations
✍ Scribed by Naoyasu Kita
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 152 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0362-546X
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✦ Synopsis
This paper studies the large time behavior of the small solution to the nonlinear Schr odinger equation with power type nonlinearity. If the power is large enough, then it is well known that the nonlinear solution asymptotically behaves like a linear solution as t → ± ∞ (see e.g.
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