Long-Time Asymptotics for the integrable discrete nonlinear Schr\"odinger equation: The Focusing Case
Mathematical Physics
2016-10-19 v4 math.MP
Abstract
We investigate the long-time asymptotics for the focusing integrable discrete nonlinear Schr\"odinger equation. Under generic assumptions on the initial value, the solution is asymptotically a sum of 1-solitons. We find different phase shift formulas in different regions. Along rays away from solitons, the behavior of the solution is decaying oscillation. This is one way of stating the soliton resolution conjecture. The proof is based on the nonlinear steepest descent method.
Keywords
Cite
@article{arxiv.1512.01760,
title = {Long-Time Asymptotics for the integrable discrete nonlinear Schr\"odinger equation: The Focusing Case},
author = {Hideshi Yamane},
journal= {arXiv preprint arXiv:1512.01760},
year = {2016}
}
Comments
22 pages, 2 figures