Connecting geometry, topology and spectra for finite-gap NLS potentials

Physica D: Nonlinear Phenomena

Volumn 152-153, Issue , 2001, Pages 9-19

  Calini, Annalisa M ^a   Ivey, Thomas A ^b  

^a Department of Teacher Education and Department of Sociology and Anthropology   (United States)

^b BALL STATE UNIVERSITY   (United States)

Author keywords

Floquet spectra; Nonlinear Schr dinger equation; Vortex filament flow

Indexed keywords

COMPUTATIONAL COMPLEXITY; CURVE FITTING; NONLINEAR EQUATIONS; SPECTRUM ANALYSIS;

FLOQUET SPECTRA; NONLINEAR SCHRODINGER EQUATIONS (NLS); VORTEX FILAMENT FLOW;

VORTEX FLOW;

EID: 18344415616     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00154-3     Document Type: Article

References (10)

1. Ablowitz M.J., Herbst B.M., Schober C.M. Computational chaos in the nonlinear Schrödinger equation without homoclinic crossings. Physica A. 228:1996;212-235.
2. E.D. Belokolos, A.I. Bobenko, V.Z. Enol'skii, A.R. Its, V.B. Matveev, Algebro-geometric Approach to Nonlinear Integrable Equations, Springer, Berlin, 1994.
3. Calini A. A note on a Bäcklund transformation for the continuous Heisenberg model. Phys. Lett. A. 203:1995;333-344.
4. A. Calini, T. Ivey, Finite-genus solutions of the vortex filament equation, in preparation.
5. Y. Fukumoto, R.L. Ricca, Vortex Filament Motion and Related Integrable Systems, World Scientific, Singapore, 1999.
6. 3 : a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the filament equation, Preprint dg-ga/9703020, 1987.
7. Hasimoto H. A soliton on a vortex filament. J. Fluid Mech. 51:1972;477-485.
8. W.B.R. Lickorish, An Introduction to Knot Theory, Springer, Berlin, 1997.
9. A. Sym, Soliton surfaces and their applications, in: Geometrical Aspects of the Einstein Equations and Integrable systems, Lecture Notes in Physics 239 (1985) 154.
10. Zakharov V.E., Shabat A.B. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP. 34:1972;62-69.