References
- Ruijsenaars , S. N. M. 2001 . Reflectionless analytic difference operators I. Algebraic framework . J. Nonlin. Math. Phys. , 8 : 106 – 138 .
- Ruijsenaars , S. N. M. 2001 . Reflectionless analytic difference operators II. Relations to soliton systems . J. Nonlin. Math. Phys. , 8 : 256 – 287 .
- Toda , M. 1981 . Theory of nonlinear lattices , Berlin : Springer .
- Flaschka , H. 1974 . On the Toda lattice. II . Progr. Theor. Phys. , 51 : 703 – 716 .
- Faddeev , L. D. and Takhtajan , L. A. 1987 . Hamiltonian methods in the theory of solitons , Berlin : Springer .
- Ruijsenaars , S. N. M. and Schneider , H. 1986 . A new class of integrable systems and its relation to solitons . Ann. Phys. (N.Y.) , 170 : 370 – 405 .
- Manakov , S. V. 1975 . Complete integrability and stochastization of discrete dynamical systems . Sov. Phys. JETP , 40 : 269 – 274 .
- Novikov , S. , Manakov , S. V. , Pitaevskii , L. P. and Zakharov , V. E. 1984 . Theory of solitons , New York : Consultants Bureau .
- Kac , M. and van Moerbeke , P. 1975 . On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices . Adv. in Math. , 16 : 160 – 169 .
- Y. B. Suris The problem of integrable discretization: Hamiltonian approach, to appear
- Santini , P. M. 1993 . “ Integrable singular integral evolution equations ” . In “Important developments in soliton theory” , Edited by: Fokas , A. S. and Zakharov , V. E. 147 – 177 . New York : Springer .
- Ruijsenaars , S. N. M. 1990 . “ Finite-dimensional soliton systems ” . In Integrable and superintegrable systems , Edited by: Kupershmidt , B. 165 – 206 . Singapore : World Scientific .
- Ruijsenaars , S. N. M. 1994 . Action-angle maps and scattering theory for some finite-dimensional integrable systems II. Solitons, antisolitons, and their bound states . Publ. RIMS Kyoto Univ. , 30 : 865 – 1008 .
- Schwarz , M. 1982 . Korteweg-de Vries and nonlinear equations related to the Toda lattice . Adv. in Math. , 44 : 132 – 154 .
- Kupershmidt B. A. Discrete Lax equations and differential-difference calculus, Astérisque 123 (Paris, 1985)
- Zeng , Y. and Rauch–Wojciechowski , S. 1995 . Continuous limits for the Kac-van Moerbeke hierarchy and for their restricted flows . J. Phys. A: Math. Gen. , 28 : 3825 – 3840 .
- Morosi , C. and Pizzocchero , L. 1996 . On the continuous limit of integrable lattices I. The Kac-Moerbeke system and KdV theory . Comm. Math. Phys. , 180 : 505 – 528 .
- S. N. M. Ruijsenaars Reflectionless analytic difference operators III. Hilbert space aspects, to appear
- Scott , A. C. , Chu , F. Y. F. and McLaughlin , D. W. 1973 . The soliton: a new concept in applied science . Proc. IEEE , 61 : 1443 – 1483 .
- Calogero , F. and Degasperis , A. 1982 . Spectral transform and solitons , Vol. I , Amsterdam : North-Holland .
- Newell , A. C. 1985 . Solitons in mathematics and physics , Philadelphia : SIAM .