Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Scopus Q: search.filters.scopusQuartile.Q3Subject: search.filters.subject.Integrable systems

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  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    Integrable Systems From Inelastic Curve Flows in 2-And 3-Dimensional Minkowski Space
    (Taylor & Francis, 2016) Alkan, Kıvılcım; Anco, Stephen C.
    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.
  • Conference Object
    Citation - WoS: 1
    Resonant Dispersive Benney and Broer-Kaup Systems in 2+1 Dimensions
    (IOP Publishing Ltd., 2014) Lee, Jyh Hao; Pashaev, Oktay
    We represent the Benney system of dispersionless hydrodynamic equations as NLS type infinite system of equations with quantum potential. We show that negative dispersive deformation of this system is an integrable system including vector generalization of Resonant NLS and 2+1 dimensional nonlocal Resonant NLS. We obtain bilinear form and soliton solutions in these systems and find the resonant character of soliton interaction. Equivalent vector Broer-Kaup system and non-local 2+1 dimensional nonlocal Broer-Kaup equation are constructed.