Model order reduction for nonlinear Schrödinger equation

AKKOYUNLU C., Uzunca M., KARASÖZEN B.

6th International Conference on Chaotic Modeling and Simulation, CHAOS 2013, İstanbul, Türkiye, 11 - 14 Haziran 2013, ss.33-40 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.33-40
  • Anahtar Kelimeler: Model order reduction, Nonlinear Schrödinger equation, Periodic solutions
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

Proper orthogonal decomposition (POD) is a method for deriving reduced order models of dynamical systems. In this paper, the POD is applied to the nonlinear Schrödinger equation (NLS). The NLS equation is discretized in space by finite differences and is solved in time either by structure preserving symplectic or energy preserving average vector field (AVF) integrators. Numerical results for one dimensional 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 phase space structure of the NLS equation.