An Approximation Method for the Scattering Data of One-Dimensional Soliton Equations under Arbitrary Rapidly-Decreasing Initial Pulses

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.

to appear in Journal of the Physical Society of Japan

References in corpus (4)

• Collisions of matter-wave solitons
• Realizing bright matter-wave soliton collisions with controlled relative phase
• Collisions of bright solitary matter waves
• Roles of Interfering Radiation Emitted from Decaying Pulses Obeying Soliton Equations Belonging to the Ablowitz-Kaup-Newell-Segur Systems