Instability of the finite‐difference split‐step method applied to the nonlinear Schrödinger equation. II. moving soliton |
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| Authors: | Taras I Lakoba |
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| Institution: | Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont |
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| Abstract: | We analyze a mechanism and features of a numerical instability (NI) that can be observed in simulations of moving solitons of the nonlinear Schrödinger equation (NLS). This NI is completely different than the one for the standing soliton. We explain how this seeming violation of the Galilean invariance of the NLS is caused by the finite‐difference approximation of the spatial derivative. Our theory extends beyond the von Neumann analysis of numerical methods; in fact, it critically relies on the coefficients in the equation for the numerical error being spatially localized. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1024–1040, 2016 |
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| Keywords: | numerical instability operator splitting nonlinear evolution equations |
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