Model order reduction for nonlinear Schrodinger equation

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2015-05-01
Karasözen, Bülent
Akkoyunlu, Canan
Uzunca, Murat
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.
Citation Formats
B. Karasözen, C. Akkoyunlu, and M. Uzunca, “Model order reduction for nonlinear Schrodinger equation,” pp. 509–519, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30498.