On the exact solution for smooth pulses of the defocusing nonlinear Schrodinger modulation equations prior to breaking
Artikel i vetenskaplig tidskrift, 2009

The modulation equations for the amplitude and the phase of the defocusing nonlinear Schrodinger (NLS) equation in the semi-classical limit are solved exactly for smooth pulse initial data using an implicit hodograph representation of Tsarev (1985 Sov. Math.-Dokl. 31 448) combined with an extension of Riemann's method on multi-sheeted characteristic planes developed by Ludford (1952 Proc. Camb. Phil. Soc. 48 499-510, 1954 J. Ration. Mech. 3 77-88). Our results extend previous exact solutions of the modulation equations for piecewise step function data (Biondini and Kodama 2006 J. Nonlinear Sci. 16 435-81, Kodama and Wabnitz 1995 Opt. Lett. 20 2291-3, Kodama 1999 SIAM J. Appl. Math. 59 2162-92) and for smooth monotone data (Wright et al 1999 Phys. Lett. A257 170-4) to more physically relevant smooth pulse data (a finite number of pulses). Our results also provide an exact characterization of the estimates for smooth pulse data of first breaking time and location, previously based on analysis of the modulation equations as hyperbolic conservation laws (Forest and McLaughlin 1998 J. Nonlinear Sci. 7 43-62). Extensions to other integrable nonlinear equations of NLS-type are also discussed in the appendix.

whitham equations

inverse scattering

oscillations

zero

fibers

method

soliton-solutions

initial data

korteweg-devries equation

small dispersion limit

semiclassical limit

Författare

M. G. Forest

The University of North Carolina System

Carl Johan Rosenberg

Chalmers, Institutionen för radio- och rymdvetenskap

O. C. Wright

Cedarville University

Nonlinearity

0951-7715 (ISSN) 13616544 (eISSN)

Vol. 22 9 2287-2308

Ämneskategorier (SSIF 2011)

Annan fysik

DOI

10.1088/0951-7715/22/9/012

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Senast uppdaterat

2025-04-04