Approximation theorem for the self-focusing Nonlinear Schrödinger Equation and for the periodic curves in R3

Physica D: Nonlinear Phenomena

Volumn 152-153, Issue , 2001, Pages 20-27

  Grinevich, P G ^a  

^a LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

Dynamics; Nonlinear Schr dinger Equation; Periodic curves; Self focussing

Indexed keywords

APPROXIMATION THEORY; CURVE FITTING; DYNAMICS; EQUATIONS OF MOTION; ERROR ANALYSIS; NONLINEAR EQUATIONS; THEOREM PROVING;

FILAMENT EQUATIONS; SELF-FOCUSING NONLINEAR SCHRODINGER EQUATIONS;

VORTEX FLOW;

EID: 18544398398     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(01)00155-5     Document Type: Article

References (15)

1. I.V. Cerednik, On the conditions of reality in finite-gap integration, Dokl. Akad. Nauk SSSR 252 (5) (1980) 1104-1108, in Russian.
2. L.D. Faddeev, L.A. Takhtajian, Hamiltonian Methods in the Theory of Solitons, Springer, Berlin, 1980.
3. Grinevich P.G., Schmidt M.U. Period preserving nonisospectral flows and the moduli space of periodic solutions of soliton equations. Physica D. 87:1995;73-98.
4. 3 : a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament equation, SFB 288 Preprint No. 254. Electronic version: dg-ga@msri.org/9703020.
5. Hasimoto R. A soliton on vortex filament. J. Fluid. Mech. 51:1972;477-485.
6. A.R. Its, V.P. Kotljarov, Explicit formulas for solutions of the Nonlinear Schrödinger Equation, Dokl. Ukrain. SSR Ser. A 11 (1976) 965-968, in Ukrainian.
7. Kamchatnov A.M. On improving the effectiveness of periodic solutions of the NLS and DNLS equations. J. Phys. A. 23(13):1990;2945-2960.
8. I.M. Krichever, The Cauchy problem for doubly periodic solutions of KP II equation, in: A. Fokas, V.E. Zakharov (Eds.), Important Developments in Soliton Theory, Springer, Berlin, 1993, pp. 123-146.
9. Marchenko V.A., Ostrovski I.V. A characterization of the spectrum of Hill's operator. Math. USSR Sb. 26(4):1975;493-554.
10. Novikov S.P. The periodic Korteveg-de Vries problem. I. Funct. Anal. Appl. 8:1974;236-246.
11. Previato E. Hyperelliptic quasi-periodic and soliton solutions of the Nonlinear Schrödinger Equation. Duce Math. J. 52(2):1985;329-377.
12. M.U. Schmidt, Integrable Systems and Riemann Surfaces of Infinite Genus, Memoirs of the American Mathematical Society, 1996, p. 551.
13. Sym A. Vortex filament motion in terms of Jacobi theta functions. Fluid Dyn. Res. 3:1988;151-156.
14. V.E. Zakharov, S.V. Manakov, S.P. Novikov, L.P. Pitaevsky, Soliton Theory, Plenum Press, New York, 1984.
15. 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.