Equations of the inverse problem, Backlund transformations, and the theory of connections

Journal of Mathematical Sciences

Volumn 94, Issue 5, 1999, Pages 1685-1699

  Rybnikov, A K ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0343154438     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/BF02365073     Document Type: Review

References (17)

1. A. M. Vasil'ev, Theory of Geometrical-Differential Structures, Moscow University Press, Moscow (1987).
2. L. E. Evtushik, Yu. G. Lumiste, N. M. Ostianu, and A. N. Shirokov, "Geometrical-differential structures on manifolds," Probl. Geom. Itogi Nauki. VINITI Akad. Nauk SSSR, 9, 5-246 (1979).
3. V. E. Zakharov and L. A. Takhtajan, "Equivalence of the nonlinear Schrödinger equation and Heisenberg ferromagnetic equations," Teor. Mat. Fiz., 38, No. 1, 26-35 (1979).
4. G. F. Laptev, "Differential geometry of submerged manifolds," Tr. Mosk. Mat. Obshch., No. 2, 275-382 (1953).
5. G. F. Laptev, "Theoretic-group method of geometrical-differential investigations," Proc. 3rd All-Union Math. Congress, 1956, Moscow, Akad. Nauk SSSR, No. 3, 409-418 (1958).
6. G. F. Laptev, "The main higher-order infinitesimal structures on a smooth manifold," Tr. Geom. Sem. VINITI, Akad. Nauk SSSR, No. 1, 139-189 (1966).
7. G. F. Laptev, "Structural equations of the principal bundle of a manifold," Tr. Geom. Sem. VINITI, Akad. Nauk SSSR, No. 2, 161-178 (1969).
8. G. F. Laptev, "On the invariant analytical theory of differentiable mappings," Tr. Geom. Sem. VINITI, Akad. Nauk SSSR, No. 6, 37-42 (1974).
9. A. K. Rybnikov, "On the geometry of pseudodifferentials of evolutionary equations," Izv. Vuzov. Mat., No. 5, 55-67 (1995).
10. L. A. Takhtajan and L. D. Faddeev, The Hamiltonian Approach in Soliton Theory [in Russian], Nauka, Moscow (1987).
11. M. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).
12. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations, Academic Press, London (1984).
13. F. B. Estabrook and H. D. Wahlquist, "Prolongation structures, connection theory and Backlund transformation," in: Nonlinear evolution equations solvable by the spectral transform, (F. Calogero, ed.), Res. Notes Math., 26, Pitman, London (1978).
14. R. Hermann, "Pseudodifferentials of Estabrook and Wahlquist, the geometry of solutions, and the theory of connections," Phys. Rev. Lett., 36, No. 15, 835-836 (1976).
15. R. Hermann, The Geometry of Non-linear Differential Equations, Backlund Transformations, and Solitons, Math. Sci. Press, New York (1976).
16. S. Kobayashi and K. Nomizu, Foundation of Differential Geometry, 1, Interscience Publ., New York (1963).
17. H. D. Wahlquist and F. B. Estabrook, "Prolongation structures of nonlinear evolution equations," J. Math. Phys., 16, No. 1, 1-7 (1975).