메뉴 건너뛰기




Volumn 37, Issue 8, 1996, Pages 3982-3996

Integrable discretizations of the Bogoyavlensky lattices

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030495725     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531611     Document Type: Article
Times cited : (22)

References (28)
  • 1
    • 0002859048 scopus 로고
    • Integrable systems with discrete time and difference operators
    • A. P. Veselov, "Integrable systems with discrete time and difference operators," Funct. Anal. Appl. 22, 1-13 (1988); J. Moser and A. P. Veselov, "Discrete versions of some classical integrable systems and factorization of matrix polynomials," Commun. Math. Phys. 139, 217-243 (1991), P. Deift, L.-Ch. Li, and C. Tomei, "Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions," Mem. Am. Math. Soc., No. 479 (1992).
    • (1988) Funct. Anal. Appl. , vol.22 , pp. 1-13
    • Veselov, A.P.1
  • 2
    • 0000008977 scopus 로고
    • Discrete versions of some classical integrable systems and factorization of matrix polynomials
    • A. P. Veselov, "Integrable systems with discrete time and difference operators," Funct. Anal. Appl. 22, 1-13 (1988); J. Moser and A. P. Veselov, "Discrete versions of some classical integrable systems and factorization of matrix polynomials," Commun. Math. Phys. 139, 217-243 (1991), P. Deift, L.-Ch. Li, and C. Tomei, "Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions," Mem. Am. Math. Soc., No. 479 (1992).
    • (1991) Commun. Math. Phys. , vol.139 , pp. 217-243
    • Moser, J.1    Veselov, A.P.2
  • 3
    • 0041091600 scopus 로고
    • Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions
    • A. P. Veselov, "Integrable systems with discrete time and difference operators," Funct. Anal. Appl. 22, 1-13 (1988); J. Moser and A. P. Veselov, "Discrete versions of some classical integrable systems and factorization of matrix polynomials," Commun. Math. Phys. 139, 217-243 (1991), P. Deift, L.-Ch. Li, and C. Tomei, "Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions," Mem. Am. Math. Soc., No. 479 (1992).
    • (1992) Mem. Am. Math. Soc. , vol.479
    • Deift, P.1    Li, L.-Ch.2    Tomei, C.3
  • 4
    • 0000436031 scopus 로고
    • Integrable mappings and nonlinear integrable lattice equations
    • V. Papageorgiou, F. Nijhoff, and H. Capel, "Integrable mappings and nonlinear integrable lattice equations," Phys. Lett. A 147, 106-114 (1990); "Complete integrability of Lagrangian mappings and lattices of KdV type," Phys. Lett. A 155, 377-387 (1991); "Integrable time-discrete systems: lattices and mappings," Lect. Notes Math. 1510, 312-325 (1992).
    • (1990) Phys. Lett. A , vol.147 , pp. 106-114
    • Papageorgiou, V.1    Nijhoff, F.2    Capel, H.3
  • 5
    • 30244570952 scopus 로고
    • Complete integrability of Lagrangian mappings and lattices of KdV type
    • V. Papageorgiou, F. Nijhoff, and H. Capel, "Integrable mappings and nonlinear integrable lattice equations," Phys. Lett. A 147, 106-114 (1990); "Complete integrability of Lagrangian mappings and lattices of KdV type," Phys. Lett. A 155, 377-387 (1991); "Integrable time-discrete systems: lattices and mappings," Lect. Notes Math. 1510, 312-325 (1992).
    • (1991) Phys. Lett. A , vol.155 , pp. 377-387
  • 6
    • 0000436031 scopus 로고
    • Integrable time-discrete systems: Lattices and mappings
    • V. Papageorgiou, F. Nijhoff, and H. Capel, "Integrable mappings and nonlinear integrable lattice equations," Phys. Lett. A 147, 106-114 (1990); "Complete integrability of Lagrangian mappings and lattices of KdV type," Phys. Lett. A 155, 377-387 (1991); "Integrable time-discrete systems: lattices and mappings," Lect. Notes Math. 1510, 312-325 (1992).
    • (1992) Lect. Notes Math. , vol.1510 , pp. 312-325
  • 7
    • 0000582507 scopus 로고
    • Generalized Toda chains in discrete time
    • Yu. B. Suris, "Generalized Toda chains in discrete time," Leningrad Math. J. 2, 339-352 (1991); "Discrete-time generalized Toda lattices: complete integrability and relation with relativistic Toda lattices," Phys. Lett. A 145, 113-119 (1990).
    • (1991) Leningrad Math. J. , vol.2 , pp. 339-352
    • Suris, Yu.B.1
  • 8
    • 30244465184 scopus 로고
    • Discrete-time generalized Toda lattices: Complete integrability and relation with relativistic Toda lattices
    • Yu. B. Suris, "Generalized Toda chains in discrete time," Leningrad Math. J. 2, 339-352 (1991); "Discrete-time generalized Toda lattices: complete integrability and relation with relativistic Toda lattices," Phys. Lett. A 145, 113-119 (1990).
    • (1990) Phys. Lett. A , vol.145 , pp. 113-119
  • 9
    • 0009286251 scopus 로고
    • A simple method to generate integrable symplectic maps
    • edited by I. Antoniou and F. J. Lambert Springer, New York
    • O. Ragnisco, "A simple method to generate integrable symplectic maps," in Solitons and chaos, edited by I. Antoniou and F. J. Lambert (Springer, New York, 1991), pp. 227-231; "A discrete Neumann system," Phys. Lett. A 167, 165-171 (1992); "Dynamical r-matrices for integrable maps," Phys. Lett. A 198, 295-305 (1995).
    • (1991) Solitons and Chaos , pp. 227-231
    • Ragnisco, O.1
  • 10
    • 0000792376 scopus 로고
    • A discrete Neumann system
    • O. Ragnisco, "A simple method to generate integrable symplectic maps," in Solitons and chaos, edited by I. Antoniou and F. J. Lambert (Springer, New York, 1991), pp. 227-231; "A discrete Neumann system," Phys. Lett. A 167, 165-171 (1992); "Dynamical r-matrices for integrable maps," Phys. Lett. A 198, 295-305 (1995).
    • (1992) Phys. Lett. A , vol.167 , pp. 165-171
  • 11
    • 30244488487 scopus 로고
    • Dynamical r-matrices for integrable maps
    • O. Ragnisco, "A simple method to generate integrable symplectic maps," in Solitons and chaos, edited by I. Antoniou and F. J. Lambert (Springer, New York, 1991), pp. 227-231; "A discrete Neumann system," Phys. Lett. A 167, 165-171 (1992); "Dynamical r-matrices for integrable maps," Phys. Lett. A 198, 295-305 (1995).
    • (1995) Phys. Lett. A , vol.198 , pp. 295-305
  • 12
    • 0000422645 scopus 로고
    • A discrete-time Garnier system
    • Yu. B. Suris, "A discrete-time Garnier system," Phys. Lett. A 189, 281-289 (1994); "A family of integrable standard- like maps related to symmetric spaces," Phys. Lett. A 192, 9-16 (1994); "Discrete-time analogs of some nonlinear oscillators in an inverse-square potential," J. Phys. 27, 8161-8169 (1994).
    • (1994) Phys. Lett. A , vol.189 , pp. 281-289
    • Suris, Yu.B.1
  • 13
    • 0039312303 scopus 로고
    • A family of integrable standard-like maps related to symmetric spaces
    • Yu. B. Suris, "A discrete-time Garnier system," Phys. Lett. A 189, 281-289 (1994); "A family of integrable standard-like maps related to symmetric spaces," Phys. Lett. A 192, 9-16 (1994); "Discrete-time analogs of some nonlinear oscillators in an inverse-square potential," J. Phys. 27, 8161-8169 (1994).
    • (1994) Phys. Lett. A , vol.192 , pp. 9-16
  • 14
    • 21844520798 scopus 로고
    • Discrete-time analogs of some nonlinear oscillators in an inverse-square potential
    • Yu. B. Suris, "A discrete-time Garnier system," Phys. Lett. A 189, 281-289 (1994); "A family of integrable standard- like maps related to symmetric spaces," Phys. Lett. A 192, 9-16 (1994); "Discrete-time analogs of some nonlinear oscillators in an inverse-square potential," J. Phys. 27, 8161-8169 (1994).
    • (1994) J. Phys. , vol.27 , pp. 8161-8169
  • 15
    • 0039479920 scopus 로고    scopus 로고
    • A time discretized version of the Calogero-Moser model
    • F. Nijhoff and G.-D. Pang, "A time discretized version of the Calogero-Moser model," Phys. Lett. A 191, 101-107 (1994); "Discrete-time Calogero-Moser model and lattice KP equation," in Proceedings of the International Workshop Symmetries and Integrability of Difference Equations edited by D. Levi, L. Vinet, P. Winternitz (to appear).
    • (1994) Phys. Lett. A , vol.191 , pp. 101-107
    • Nijhoff, F.1    Pang, G.-D.2
  • 16
    • 0039479920 scopus 로고    scopus 로고
    • Discrete-time Calogero-Moser model and lattice KP equation
    • edited by D. Levi, L. Vinet, P. Winternitz (to appear)
    • F. Nijhoff and G.-D. Pang, "A time discretized version of the Calogero-Moser model," Phys. Lett. A 191, 101-107 (1994); "Discrete-time Calogero-Moser model and lattice KP equation," in Proceedings of the International Workshop Symmetries and Integrability of Difference Equations edited by D. Levi, L. Vinet, P. Winternitz (to appear).
    • Proceedings of the International Workshop Symmetries and Integrability of Difference Equations
  • 17
    • 0030551796 scopus 로고    scopus 로고
    • Integrable time-discretization of the Ruijsenaars-Schneider model
    • F. Nijhoff, O. Ragnisco, and V. Kuznetsov, "Integrable time-discretization of the Ruijsenaars-Schneider model," Commun. Math. Phys. 176, 681-700 (1996).
    • (1996) Commun. Math. Phys. , vol.176 , pp. 681-700
    • Nijhoff, F.1    Ragnisco, O.2    Kuznetsov, V.3
  • 18
    • 0000404004 scopus 로고
    • Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice
    • Yu. B. Suris, "Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice," Phys. Lett. A 206, 153-161 (1995).
    • (1995) Phys. Lett. A , vol.206 , pp. 153-161
    • Suris, Yu.B.1
  • 19
    • 0009430264 scopus 로고    scopus 로고
    • A discrete-time relativistic Toda lattice
    • Yu B. Suris, "A discrete-time relativistic Toda lattice," J. Phys. A 29, 451-465 (1996).
    • (1996) J. Phys. A , vol.29 , pp. 451-465
    • Suris, Yu.B.1
  • 21
    • 0347113068 scopus 로고
    • On some constructions of integrable systems
    • O. I. Bogoyavlensky, "On some constructions of integrable systems," USSR Math. Izv. 31, 435 (1988); 32, 39 (1989).
    • (1988) USSR Math. Izv. , vol.31 , pp. 435
    • Bogoyavlensky, O.I.1
  • 22
    • 0345851927 scopus 로고
    • O. I. Bogoyavlensky, "On some constructions of integrable systems," USSR Math. Izv. 31, 435 (1988); 32, 39 (1989).
    • (1989) USSR Math. Izv. , vol.32 , pp. 39
  • 23
    • 0001113646 scopus 로고
    • Soliton solution to extended Volterra equations
    • K. Narita, "Soliton solution to extended Volterra equations," J. Phys. Soc. Jpn. 51, 1682-1685 (1982).
    • (1982) J. Phys. Soc. Jpn. , vol.51 , pp. 1682-1685
    • Narita, K.1
  • 24
    • 0000192657 scopus 로고
    • Integrals of a Lotka-Volterra system of odd number of variables
    • Y. Itoh, "Integrals of a Lotka-Volterra system of odd number of variables," Prog. Theor. Phys. 78, 507-510 (1987).
    • (1987) Prog. Theor. Phys. , vol.78 , pp. 507-510
    • Itoh, Y.1
  • 25
    • 0038840710 scopus 로고
    • On the r-matrix interpretation of Bogoyavlensky lattices
    • Yu. B. Suris, "On the r-matrix interpretation of Bogoyavlensky lattices," Phys. Lett. A 188, 256-262 (1994).
    • (1994) Phys. Lett. A , vol.188 , pp. 256-262
    • Suris, Yu.B.1
  • 26
    • 62649171049 scopus 로고
    • An extension and discretization of Volterra equation
    • NLP 92-90
    • S. Tsujimoto, R. Hirota, and S. Oishi, "An extension and discretization of Volterra equation," Tech. Report IEICE, NLP 92-90 (1993).
    • (1993) Tech. Report IEICE
    • Tsujimoto, S.1    Hirota, R.2    Oishi, S.3
  • 27
    • 0030164180 scopus 로고    scopus 로고
    • On some integrable discrete time systems associated with the Bogoyavlensky lattices
    • V. Papageorgiou and F. W. Nijhoff, "On some integrable discrete time systems associated with the Bogoyavlensky lattices," Phys. A 228, 172-188 (1996).
    • (1996) Phys. A , vol.228 , pp. 172-188
    • Papageorgiou, V.1    Nijhoff, F.W.2
  • 28
    • 36449007071 scopus 로고
    • Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure
    • H. Zhang, G. Tu, W. Oevel, and B. Fuchssteiner, "Symmetries, conserved quantities, and hierarchies for some lattice systems with soliton structure," J. Math. Phys. 33, 1908-1918 (1991).
    • (1991) J. Math. Phys. , vol.33 , pp. 1908-1918
    • Zhang, H.1    Tu, G.2    Oevel, W.3    Fuchssteiner, B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.