Model order reduction for nonlinear Schrodinger equation - Karasözen, Bülent; Akkoyunlu, Canan; Uzunca, Murat (Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 USA, 2015)
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. (C) 2015 Elsevier Inc. All rights reserved.
Keywords: Nonlinear Schrodinger equation; Proper orthogonal decomposition; Model order reduction; Error analysis