Abstract
Methods to detect solitons and determine their parameters are considered. The first simple observational test for soliton identification is based on the determination of statistical relationships between amplitude, duration, and carrying frequency of the detected signals, and their comparison with the relevant relationships from the soliton theory. The second method is based on the solution of the direct scattering problem for the relevant nonlinear equations. As an example the Derivative Nonlinear Schrödinger (DNLS) equation has been considered. The integral reflection coefficient, which should rapidly drop when a signal is close to the N-soliton profile, has been used as a soliton detector. Application of this technique to numerically simulated signals shows that it is more efficient than the standard Fourier transform and can be used as a practical tool for the analysis of outputs from nonlinear systems.
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Mazur, N.G., Pilipenko, V.A., Glassmeier, KH. (2008). Methods to Detect Solitons in Geophysical Signals: The Case of the Derivative Nonlinear Schrödinger Equation. In: Donner, R.V., Barbosa, S.M. (eds) Nonlinear Time Series Analysis in the Geosciences. Lecture Notes in Earth Sciences, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78938-3_14
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DOI: https://doi.org/10.1007/978-3-540-78938-3_14
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