In this thesis, we study single and coupled
  nonlinear Schrödinger equations with periodic boundary
  conditions in multi-symplectic form and integrate them in space by
  pseudospectral Fourier method and in time by implicit midpoint
  rule. The multi-symplectic form in space and time, the local
  energy and momentum of the underlying partial differential
  equations are conserved in long time integration very well, which
  leads to conservation of global energy and momentum. The numerical
  results obtained for various examples of single and coupled
  nonlinear Schrödinger equations confirm the highly accurate
  local and global preservation properties of the multi-symplectic
  pseudospectral Fourier method in long term integration.
 

  Keywords : Nonlinear Schrödinger equation, Hamiltonian
  equations, pseudospectral Fourier method, symplectic integration,
  multi-symplectic pde's

  GECMEN, ZERRIN
  Yüksek Lisans, Matematik
  Supervisor : Prof. Dr. Bülent KARASÖZEN
  Co-supervisor :
  Nisan 2002, 75 sayfa

  Bu tezde, coklu simplektik yapi daki
  dogrusal olmayan tekli ve ikili periyodik sinir
  degerlere sahip Schödinger denklemini uzay
  degiskeninde sözde Fourier spektral, zaman
  degiskeninde ise orta nokta Euler yöntemi ile ayri
  klastirilmistir. Kismi türevli dogrusal
  olmayan Schrödinger denkleminin hem yerel hem de genel enerji ve
  momenti uzun zaman araliginda korunmustur. Farkli tek
  ve ikili dogrusal olmayan Schödinger denklemi örneklerinde
  elde edilen sayisal sonuclar da simplektik Fourier
  yönteminin yerel ve genel enerji ve momenti korudugunu
  dogrulamistir.

  Anahtar Kelimeler : Dogrusal olmayan Schödinger
  denklemi, Hamilton kismi türevli denklemler, sözde Fourier
  spektral yöntem, coklu simpektik kismi türevli denklemler