Model order reduction for nonlinear Schrodinger equation

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2015-05-01

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Karasözen, Bülent
Uzunca, Murat

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We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reproduce very well the characteristic dynamics of the system, such as preservation of energy and the solutions.

Subject Keywords

Nonlinear Schr¨odinger equation, Proper orthogonal decomposition, Model order reduction, Error analysis

URI

https://hdl.handle.net/11511/30498

Journal

APPLIED MATHEMATICS AND COMPUTATION

DOI

https://doi.org/10.1016/j.amc.2015.02.001

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Graduate School of Applied Mathematics, Article

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Citation Formats

B. Karasözen and M. Uzunca, “Model order reduction for nonlinear Schrodinger equation,” APPLIED MATHEMATICS AND COMPUTATION, pp. 509–519, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30498.