Model order reduction for nonlinear Schrodinger equation

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KARASÖZEN B., Akkoyunlu C., Uzunca M.

APPLIED MATHEMATICS AND COMPUTATION, vol.258, pp.509-519, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 258
  • Publication Date: 2015
  • Doi Number: 10.1016/j.amc.2015.02.001
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.509-519
  • Middle East Technical University Affiliated: Yes


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.