TY - JOUR

T1 - Asymptotic behavior of the nonlinear Schrödinger equation with rapidly varying, mean-zero dispersion

AU - Bronski, Jared C.

AU - Kutz, J. Nathan

N1 - Funding Information:
Two distinct and well-understood possibilities arise for the soliton propagation \[1 -3\].In the case where the coefficient multiplying the dispersion is positive, the focusing case, the fundamental soliton solutions can be characterized by nonlinear bound states which are hyperbolic secant solutions (bright solitons). When the dispersion coefficient * Corresponding author. Acknowledges support from a National Science Foundation Postdoctoral Fellowship (DMS-9407473). 1 Also with AT&T Research and Lucent Technologies, Bell Laboratories, Murray Hill, NJ 07974, USA, and acknowledges support from a National Science Foundation University-Industry Postdoctoral Fellowship (DMS-9508664).

PY - 1997

Y1 - 1997

N2 - In this paper we consider the nonlinear Schrödinger equation with an oscillatory, mean-zero dispersion, which has recently been proposed as an alternative method of dispersion compensation for pulse transmission in optical fibers. Under the assumption that the time scale on which the dispersion changes is short in comparison with the dispersion and nonlinearity time scales, we are able to factor out the leading order contribution of the dispersion which leads to an effective equation for the pulse dynamics. This effective equation is a nonlinear diffusion equation, which is shown by an amplitude-phase decomposition to reduce to the well-known porous medium equation for the amplitude dynamics and a linear, nonconstant coefficient diffusion equation for the phase which is driven by the amplitude.

AB - In this paper we consider the nonlinear Schrödinger equation with an oscillatory, mean-zero dispersion, which has recently been proposed as an alternative method of dispersion compensation for pulse transmission in optical fibers. Under the assumption that the time scale on which the dispersion changes is short in comparison with the dispersion and nonlinearity time scales, we are able to factor out the leading order contribution of the dispersion which leads to an effective equation for the pulse dynamics. This effective equation is a nonlinear diffusion equation, which is shown by an amplitude-phase decomposition to reduce to the well-known porous medium equation for the amplitude dynamics and a linear, nonconstant coefficient diffusion equation for the phase which is driven by the amplitude.

KW - Method of stationary phase

KW - Nonlinear schrödinger equation

KW - Optical fibers

KW - Porous medium equation

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U2 - 10.1016/S0167-2789(97)00019-5

DO - 10.1016/S0167-2789(97)00019-5

M3 - Article

AN - SCOPUS:0342481154

VL - 108

SP - 315

EP - 329

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -