Number of solitons produced from a large initial pulse in the generalized NLS dispersive hydrodynamics theory

TL;DR

This paper derives an analytical formula to predict the number of solitons generated from a large initial pulse in a generalized NLS dispersive hydrodynamics framework, extending previous results for integrable systems.

Contribution

It provides a generalized asymptotic formula for soliton count applicable to non-integrable equations within the generalized NLS class.

Findings

Analytical prediction of soliton number from initial pulse

Extension of inverse scattering results to generalized NLS equations

Applicable to large initial pulses in dispersive hydrodynamics

Abstract

We show that the number of solitons produced from an arbitrary initial pulse of the simple wave type can be calculated analytically if its evolution is governed by a generalized nonlinear Schr\"{o}dinger equation provided this number is large enough. The final result generalizes the asymptotic formula derived for completely integrable nonlinear wave equations like the standard NLS equation with the use of the inverse scattering transform method.