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Phys Rev Lett. 2003 Mar 21;90(11):113902. Epub 2003 Mar 21.

Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients.

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Physics Department, The University of Auckland, Private Bag 92019, Auckland, New Zealand.


A broad class of exact self-similar solutions to the nonlinear Schrödinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.

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