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

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 Schrödinger 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.

6 pages, 2 figures

References in corpus (4)

• The theory of optical dispersive shock waves in photorefractive media
• Gurevich-Pitaevskii problem and its development
• Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse
• Propagation of wave packets along intensive simple waves

Cited by in corpus (3)

• Asymptotic theory of not completely integrable soliton equations
• Quasiclassical integrability condition in AKNS scheme
• Modulation theory for the sine-Gordon equation