TY - JOUR

T1 - Soliton perturbations and the random Kepler problem

AU - Abdullaev, F. Kh

AU - Bronski, J. C.

AU - Papanicolaou, G.

N1 - Funding Information:
We acknowledge partial support by the US Civilian Research & Development Foundation (Award ZM1-342), by the NSF Postdostoral Fellowship Program grant DMS 94-07473, by AFOSR grant F49620-98-1-0211 and by NSF grant DMS-9622854.

PY - 2000/1/15

Y1 - 2000/1/15

N2 - We consider the influence of randomly varying parameters on the propagation of solitons for the one-dimensional nonlinear Schrödinger equation. This models, for example, optical soliton propagation in a fiber whose properties vary with distance along the fiber. By using an averaged Lagrangian approach we obtain a system of stochastic modulation equations for the evolution of the soliton parameters, which takes the form of a randomly perturbed Kepler problem. We use the action-angle formulation of the Kepler problem to calculate the statistics of the escape time. The mean escape time for the Kepler problem corresponds, in the optical context, to the expected distance until the soliton disintegrates.

AB - We consider the influence of randomly varying parameters on the propagation of solitons for the one-dimensional nonlinear Schrödinger equation. This models, for example, optical soliton propagation in a fiber whose properties vary with distance along the fiber. By using an averaged Lagrangian approach we obtain a system of stochastic modulation equations for the evolution of the soliton parameters, which takes the form of a randomly perturbed Kepler problem. We use the action-angle formulation of the Kepler problem to calculate the statistics of the escape time. The mean escape time for the Kepler problem corresponds, in the optical context, to the expected distance until the soliton disintegrates.

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U2 - 10.1016/S0167-2789(99)00118-9

DO - 10.1016/S0167-2789(99)00118-9

M3 - Article

AN - SCOPUS:0348193007

SN - 0167-2789

VL - 135

SP - 369

EP - 386

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3-4

ER -