Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/9351
Title: Integrable systems from inelastic curve flows in 2-and 3-dimensional Minkowski space
Authors: Alkan, Kıvılcım
Anco, Stephen C.
Keywords: Curve flow
Integrable systems
Minkowski plane
Minkowski space
Issue Date: 2016
Publisher: Taylor & Francis
Abstract: Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2-and 3- dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrodinger (NLS) equation in 2- and 3- dimensional Euclidean space, respectively. In 2-dimensional Minkowski space, time-like/space-like inelastic curve flows are shown to yield the defocusing mKdV equation and its bi-Hamiltonian integrability structure, while inelastic null curve flows are shown to give rise to Burgers' equation and its symmetry integrability structure. In 3-dimensional Minkowski space, the complex defocusing mKdV equation and the NLS equation along with their bi-Hamiltonian integrability structures are obtained from timelike inelastic curve flows, whereas spacelike inelastic curve flows yield an interesting variant of these two integrable equations in which complex numbers are replaced by hyperbolic (split-complex) numbers.
URI: https://doi.org/10.1080/14029251.2016.1175822
https://hdl.handle.net/11147/9351
ISSN: 1402-9251
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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