Journal ArticleDOI
Schrödinger flows, binormal motion for curves and the second AKNS-hierarchies
Qing Ding,Jun-ichi Inoguchi +1 more
TLDR
In this article, a unified geometric interpretation of the second AKNS-hierarchies via the geometric concept of Schrodinger flows in the category of symplectic manifolds and binormal motion for curves in the Minkowski 3-space is presented.Abstract:
In this paper, we present a unified geometric interpretation of the second AKNS-hierarchies via the geometric concept of Schrodinger flows in the category of symplectic manifolds and binormal motion for curves in the Minkowski 3-space.read more
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Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations
TL;DR: In this paper, the evolution equations of the magnetic field and electric field vectors of polarized light ray propagating along a coiled optical fiber in Minkowski space were obtained and new kinds of binormal motions and Hasimoto transformations were defined to relate these evolution equations into the nonlinear Schrodinger's equation.
Journal ArticleDOI
Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in the ordinary space
TL;DR: In this paper, the evolution equations of the electric field and magnetic field vectors of the polarized light ray traveling in a coiled optical fiber in the ordinary space into the non-linear space were derived.
Journal ArticleDOI
Polarization of propagated light with optical solitons along the fiber in de-sitter space S12
TL;DR: In this article, the authors presented transformation equations for electromagnetic fields of polarized light ray traveling by magnetic optical fiber on De Sitter space S 1 2, where the new spherical frame of some Lorentzian spherical systems that are illustrated simultaneously with co-ciled magnetic optical fibre was illustrated in De Satter space.
Journal ArticleDOI
Geometry of Hasimoto Surfaces in Minkowski 3-Space
Melek Erdoğdu,Mustafa Özdemir +1 more
TL;DR: In this article, the Gaussian and mean curvature of Hasimoto surfaces in Minkowski 3-space were investigated for three cases, and the characterization of parameter curves of the Hasimoto surface was given.
Journal ArticleDOI
Differential Geometric Approach of Betchow-Da Rios Soliton Equation
TL;DR: In this article , the authors investigate differential geometric properties of the soliton surface M associated with the Betchow-Da Rios Equation and give derivative formulas of the Frenet frame of unit speed curve Φ = Φ(s,t) for all t. They also discuss the linear map of Weingarten type in the tangent space of the surface that generates two invariants: k and h.
References
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The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
Book
Hamiltonian methods in the theory of solitons
L. D. Faddeev,Leon A. Takhtajan +1 more
TL;DR: The Nonlinear Schrodinger Equation (NS Model) and Zero Curvature Representation (ZCR) as discussed by the authors have been used for the classification and analysis of Integrable Evolution Equations.
Journal ArticleDOI
A soliton on a vortex filament
TL;DR: In this article, the intrinsic equation governing the curvature K and the torsion τ of an isolated very thin vortex filament without stretching in an incompressible inviscid fluid is reduced to a non-linear Schrodinger equation.
Journal ArticleDOI
Continuum spin system as an exactly solvable dynamical system
TL;DR: In this paper, it was shown that the one-dimensional classical spins with nearest neighbor Heisenberg interaction is an exactly solvable system and its dynamics describable by the nonlinear Schrodinger equation.