Motion of an integral curve of a Hamiltonian dynamical system and the evolution equations in 3D

Bayrakdar T., ERGİN A. A.

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, cilt.14, sa.12, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 12
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1142/s0219887817501729
  • Dergi Adı: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Hamiltonian dynamical system, Poisson structure, motion of curves, Darboux frame, geodesic, Hashimoto function, SOLITON
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We show that all of the nonstretching curve motions specified in the Frenet-Serret frame in the literature can be described by the time evolution of an integral curve of a Hamiltonian dynamical system such that the underlying curve is a geodesic curve on a leaf of the foliation determined by the Poisson structure in three dimensions. As an illustrative example, we show that the focusing version of the nonlinear Schrodinger equation and the complex modified Korteweg-de Vries (mKdV) equation are obtained in this way.