Spectral splitting method for nonlinear Schrödinger equations with singular potential |
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Authors: | Andrea Sacchetti |
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Affiliation: | aDipartimento di Matematica Pura ed Applicata, Universitá di Modena e Reggio Emilia, Via Campi 213/B, Modena 41100, Italy |
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Abstract: | We consider the time-dependent one-dimensional nonlinear Schrödinger equation with pointwise singular potential. By means of spectral splitting methods we prove that the evolution operator is approximated by the Lie evolution operator, where the kernel of the Lie evolution operator is explicitly written. This result yields a numerical procedure which is much less computationally expensive than multi-grid methods previously used. Furthermore, we apply the Lie approximation in order to make some numerical experiments concerning the splitting of a soliton, interaction among solitons and blow-up phenomenon. |
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Keywords: | Nonlinear Schrö dinger equations Spectral splitting |
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