Reality conditions of loop solitons genus g: Hyperelliptic am functions

Electronic Journal of Differential Equations

Volumn 2007, Issue , 2007, Pages 1-12

  Matsutani, Shigeki ^a  

^a NONE   (Japan)

Author keywords

Elastica; Hyperelliptic functions; Loop soliton; Reality condition

Indexed keywords

EID: 34250686230     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. H. F. Baker; On the hyperelliptic sigma functions, Amer. J. of Math., Vol.XX (1898), 301-384.
2. L. Euler; Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes 1744, Leonhardi Euleri Opéra Omnia Ser. 1 Vol. 14.
3. P. G. Grinevich and S. P. Novikov; Topological charge of the real periodic finite-gap sine-Gordon solutions, Comm. Pure. Appl. Math. , Vol.56 (2003), 956-978.
4. S. Matstutani; Statistical Mechanics of Elastica on plane: Origin of MKdV hierarchy J. Phys. A, Vol.31 (1998), 2706-2725.
5. S. Matstutani; Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica, J. Geom. Phys., Vol. 43(2002), 146-162.
6. S. Matstutani; On the Moduli of a Quantized Elastica in ℙ and KdV Flows: Study of Hyperelliptic Curves as an Extension of Euler's Perspective of Elastica I, Rev. Math. Phys., Vol. 15, 559-628.
7. D. Mumford; Elastica and Computer Vision in Algebraic Geometry and its Applications, edited by C. Bajaj, Springer-Verlag, Berlin (1993), 507-518.
8. S. M. Natanzon; Real nonsingular finite zone solutions of soliton equations, Topics in topology and mathematical physics, Amer. Math. Soc. Transl. Ser. 2, 170, (1995), 153-183.
9. E. Previato; Geometry of the Modified KdV Equation in Geometric and Quantum Aspects of Integrable System, edited by G. F. Helminck, Springer-Verlag, Berlin (1993) 43-65.
10. V. Prasolov and Y. Solovyev; Elliptic Functions and Elliptic Integrals (1991) translated by D. Leites, AMS (1997).
11. C. Truesdell The rational mechanics of flexible or elastic bodies 1638-1788, Leonhardi Euleri Opera Omnia Ser. II, Vol. 11 part 2, Grell Füssli, Zürich, 1960.
12. H. Tsuru and M. Wadati; Elastic Model of Highly Supercoiled DNA Biopolymers, Vol. 25 (1986), 2083-2096.
13. K. Weierstrass; Zur Theorie der Abel'schen Functionen, Aus dem Crelle'schen Journal, Vol. 47 (1854).