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5 April 2000 Detailed resolution of the nonlinear Schrodinger equation using the full adaptive wavelet transform
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The propagation of optical pulses in nonlinear optical fibers is described by the nonlinear Schrodinger (NLS) equation. This equation can generally be solved exactly using the inverse scattering method, or for more detailed analysis, through the use of numerical techniques. Perhaps the best known numerical technique for solving he NLS equation is the split-step Fourier method, which effects a solution by assuming that the dispersion and nonlinear effects act independently during pulse propagation along the fiber. In this paper we describe an alternative numerical solution to the NLS equation using an adaptive wavelet transform technique, done entirely in the wavelet domain. This technique differs form previous work involving wavelet solutions tithe NLS equation in that these previous works used a 'split-step wavelet' method in which the linear analysis was performed in the wavelet domain while the nonlinear portion was done in the space domain. Our method takes ful advantage of the set of wavelet coefficients, thus allowing the flexibility to investigate pulse propagation entirely in either the wavelet or the space domain. Additionally, this method is fully adaptive in that it is capable of accurately tracking steep gradients which may occur during the numerical simulation.
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Mark A. Stedham and Partha P. Banerjee "Detailed resolution of the nonlinear Schrodinger equation using the full adaptive wavelet transform", Proc. SPIE 4056, Wavelet Applications VII, (5 April 2000);

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