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
Asymptotics of solutions to the time-dependent Schrödinger equation with a small Planck constant
✍ Scribed by A. S. Omuraliev
- Book ID
- 110194802
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2007
- Tongue
- English
- Weight
- 182 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0965-5425
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📜 SIMILAR VOLUMES
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.
explicit and local. Its novel features include the exact evaluation of a major contribution to an approximation to the The matrix elements of the exponential of a finite difference realization of the one-dimensional Laplacian are found exactly. This evolution operator (Eq. ( )) and a first-order ap