Roles of Interfering Radiation Emitted from Decaying Pulses Obeying Soliton Equations Belonging to the Ablowitz-Kaup-Newell-Segur Systems

TL;DR

This paper analyzes the nonlinear Schrödinger equation with box-type initial conditions, deriving analytical scattering data for interfering radiation, predicting soliton formation, and examining effects of pulse tails on wave profiles.

Contribution

It introduces an analytical approach to construct scattering data for the NLS equation with complex initial pulses, predicting soliton outcomes and unusual wave formations.

Findings

Analytical expressions for scattering data of interfering radiation

Prediction of the number of solitons formed

Conditions for double-pole soliton formation

Abstract

The nonlinear Schrodinger (NLS) equation under the box-type initial condition, which models general multiple pulses deviating from pure solitons, is analyzed. Following the approximation by splitting the initial pulse into many small bins [G. Boffetta and A. R. Osborne, J. Comp. Phys. 102, 25 (1992)], we can analyze the Zakharov-Shabat eigenvalue problem to construct transfer matrices connecting the Jost functions in each interval without direct numerical computation. We can obtain analytical expressions for the scattering data that describe interfering radiation emitted from initial pulses. The number of solitons that appear in the final stage is predicted theoretically, and the condition generating an unusual wave such as a double-pole soliton is derived. Numerical analyses under box-type initial conditions are also performed to show that the interplay between the tails from decaying pulses can affect the asymptotic profile.