On differential systems describing surfaces of constant curvature

Journal of Differential Equations

Volumn 184, Issue 1, 2002, Pages 185-214

  Ding, Qing ^a   Tenenblat, Keti ^b  

^a FUDAN UNIVERSITY   (China)

^b UNIVERSITY OF BRASILIA   (Brazil)

Author keywords

Differential systems; Evolution systems; Pseudospherical surfaces; Spherical surfaces

Indexed keywords

EID: 0036749685     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4141     Document Type: Article

References (21)

1. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The inverse scattering transform-Fourier analysis for nonlinear problems, Stud. Appl. Math. 53 (1974), 249-315.
2. R. Beals, M. Rabelo, and K. Tenenblat, Bäcklund transformations and inverse scattering solutions for some pseudospherical surfaces equations, Stud. Appl. Math. 81 (1989), 125-152.
3. J. A. Cavalcaute and K. Tenenblat, Conservation laws for nonlinear evolution equations, J. Math. Phys. 29 (1988), 1044-1049.
4. S. S. Chern and K. Tenenblat, Foliations on a surface of constant curvature and modified Korteweg-de Vries equation, J. Differential Geom. 16 (1981), 347-350.
5. S. S. Chern and K. Tenenblat, Pseudo-spherical surfaces and evolution equations, Stud. Appl. Math. 74 (1986), 55-83.
6. Q. Ding, A note on the NLS and the Schrödinger flow of maps, Phys. Lett. A 248 (1998), 49-58.
7. L. D. Faddeev and L. A. Takhtajan, "Hamiltonian Methods in the Theory of Solitons," Springer-Verlag, Berlin/Heidelberg, 1987.
8. A. P. Fordy, Derivative nonlinear Schrödinger equations and Hermitian symmetric spaces, J. Phys. A 17 (1984), 1235-1245.
9. N. N. Huang, "Soliton Theory and Perturbations," Shanghai Sciences and Technology Publishing House, Shanghai, China, 1996.
10. N. N. Huang, Z. Y. Chen, and Z. Z. Liu, The method of Darboux transformation matrix for solving Landau-Lifschitz equation for a spin chain with an easy plane, J. Phys. A 28 (1995), 4063-4082.
11. t), Stud. Appl. Math. 77 (1987), 103-117.
12. N. Kamran and K. Tenenblat, On differential equations describing pseudospherical surfaces, J. Differential Equations 115 (1995), 75-98.
13. L. D. Landau and E. M. Lifschitz, Phys. Z. Sow. 8 (1935), 153.
14. H. J. Mikeska and M. Steiner, Solitary excitations in one-dimensional magnets, Adv. in Phys. 40 (1991), 191-356.
15. A. V. Mikhailov, The Landau-Lifschitz equation and the Riemann boundary problem on a torus, Phys. Lett. A 92 (1982), 51-55.
16. M. L. Rabelo, On evolution equations which describe pseudo-spherical surfaces, Stud. Appl. Math. 81 (1989), 221-248.
17. x) which describe pseudospherical surfaces, J. Math. Phys. 31 (1990), 1400-1407.
18. xx), J. Math. Phys. 33 (1992), 537-549.
19. E. Reyes, Pseudo-spherical surfaces and integrability of evolution equations, J. Differential Equations 147 (1998), 195-230.
20. R. Sasaki, Soliton equations and pseudospherical surfaces, Nucl. Phys. B 154 (1979), 343-357.
21. M. Wadati, K. Konno, and Y. H. Ichikawa, A generalization of inverse scattering method, J. Phys. Soc. Japan 46 (1979), 1965-1966.