An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly-Decreasing Initial Pulses
Exactly Solvable and Integrable Systems
2017-06-07 v3 Pattern Formation and Solitons
Abstract
We present a novel approximation method that can predict the number of solitons asymptotically appearing under arbitrary rapidly decreasing initial wave packets. The number of solitons can be estimated without integration of the original soliton equations. As an example, we take the one-dimensional nonlinear Schrodinger equation and estimate the behaviors of the scattering amplitude in detail. The results show good agreement compared with those obtained by direct numerical integration. The presented method is applicable to a wide class of one-dimensional soliton equations.
Cite
@article{arxiv.1702.07401,
title = {An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly-Decreasing Initial Pulses},
author = {Hironobu Fujishima and Tetsu Yajima},
journal= {arXiv preprint arXiv:1702.07401},
year = {2017}
}
Comments
to appear in Journal of the Physical Society of Japan