Publications by Yuri B. SURIS

I. Books (in inverse chronological order)

2. A.I. Bobenko, Yu.B. Suris. Discrete Differential Geometry. Integrable Structure. Graduate Studies in Mathematics , Vol. 98. AMS, 2008. xxiv+404 pp. The book on the Publisher's site. Preliminary version at arXiv: math.DG/0504358

1. Yu.B. Suris. The Problem of Integrable Discretization: Hamiltonian Approach. Progress in Mathematics, Vol. 219. Basel: Birkhäuser, 2003. xxi+1070 pp. The book on the Publisher's site.

II. Papers (in inverse chronological order)

70. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Integrable discrete nets in Grassmannians. Lett. Math. Phys., 2009, 89, No. 2, p. 131-139. arXiv:0812.5102 [math.DG]

69. M. Petrera, A. Pfadler, Yu.B. Suris. On integrability of Hirota-Kimura type discretizations. Experimental study of the discrete Clebsch system. Experimental Math., 2009, 18, No. 2, p. 223-247. arXiv:0808.3345 [nlin.SI]

68. M. Petrera, Yu.B. Suris. On the Hamiltonian structure of Hirota-Kimura discretization of the Euler top. Math. Nachr. (to appear) arXiv:0707.4382 [math-ph]

67. A.I. Bobenko, Yu.B. Suris. Discrete Koenigs nets and discrete isothermic surfaces. Intern. Math. Research Notices, 2009, 2009, No. 11, p. 1976-2012. arXiv:0709.3408 [math.DG]

66. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Discrete nonlinear hyperbolic equations. Classification of integrable cases. Funkt. Analiz Prilozh., 2009, 43, p. 3-21; English translation: Funct. Anal. Appl., 2009, 43, p. 3-17. arXiv:0705.1663 [nlin.SI]

65. M. Petrera, Yu.B. Suris. An integrable discretization of the rational su(2) Gaudin model and related systems. Commun. Math. Phys., 2008, 283, p. 227-253. arXiv:0707.4088 [nlin.SI]

64. Yu.B. Suris. The discrete Green's function. - In: Discrete Differential Geometry, Eds. A.I. Bobenko, P. Schröder, J.M. Sullivan and G.M. Ziegler (Oberwolfach Seminars , Vol. 38). Basel: Birkhäuser, 2008, p. 117-133. The book on the Publisher's site.

63. A.I. Bobenko, Yu.B. Suris. Isothermic surfaces in sphere geometries as Moutard nets. Proc. Royal Soc. A , 2007, 463 , p. 3171-3193. arXiv: math.DG/0610434

62. A.I. Bobenko, Yu.B. Suris. On organizing principles of discrete differential geometry. Geometry of spheres. Uspekhi Mat. Nauk, 2007, 62, p. 3-50; English translation: Russian Math. Surveys, 2007, 62, p. 1-43. arXiv: math.DG/0608291

61. Yu.B. Suris. Toda lattices. - In: Encyclopedia of Mathematical Physics, Eds. J.-P. Françoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006, Vol. 5, p. 235-244. Encyclopedia on the Publisher's site.

60. A.I. Bobenko, D. Matthes, Yu.B. Suris. Nonlinear hyperbolic equations in surface theory: integrable discretizations and approximation results. Algebra Anal., 2005, 17, p. 53-83; English translation: St. Petersburg Math. Journal , 2006, 17, p. 39-61. arXiv: math.NA/0208042

59. A.I. Bobenko, Ch. Mercat, Yu.B. Suris. Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green's function. J. Reine Angew. Math., 2005, 583 , p. 117-161. arXiv: math.DG/0402097

58. Yu.B. Suris. Integrable lattices. - In: Encyclopedia of Nonlinear Sciences, Ed. A. Scott. New York and London: Routledge, 2004, p. 456-460. Encyclopedia on the Publisher's site.

57. V.E. Adler, Yu.B. Suris. Q4: integrable master equation related to an elliptic curve. Intern. Math. Research Notices, 2004, Nr. 47, p. 2523-2553. arXiv: nlin.SI/0309030

56. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Geometry of Yang-Baxter maps: pencils of conics and quadrirational mappings. Commun. Analysis and Geometry, 2004, 12, p. 967-1007. arXiv: math.QA/0307009

55. Yu.B. Suris. Discrete Lagrangian models. - In: Discrete Integrable Systems, Eds. B. Grammaticos, Y. Kosmann-Schwarzbach, T. Tamizhmani. Lecture Notes Phys., 2004, Vol. 644, p. 111-184.

54. A.P. Veselov, Yu.B. Suris. Lax matrices for Yang-Baxter maps. J. Nonlin. Math. Phys., 2003, 10, Suppl. 2 ( Symmetries and Integrability of Difference Equations, Eds. F.W. Nijhoff, Yu.B. Suris, C. Viallet), p. 223-230. arXiv: math.QA/0304122

53. A.I. Bobenko, D. Matthes, Yu.B. Suris. Discrete and smooth orthogonal systems: $C^\infty$-approximation. Intern. Math. Research Notices, 2003, Nr. 45, p. 2415-2459. arXiv: math.DG/0303333

52. V.E. Adler, A.I. Bobenko, Yu.B. Suris. Classification of integrable equations on quad-graphs. The consistency approach. Commun. Math. Phys., 2003, 233, p. 513-543. arXiv: nlin.SI/0202024

51. A.I. Bobenko, Yu.B. Suris. Integrable noncommutative equations on quad-graphs. The consistency approach. Lett. Math. Phys., 2002, 61, p. 241-254. arXiv: nlin.SI/0206010

50. A.I. Bobenko, Yu.B. Suris. Integrable systems on quad-graphs. Intern. Math. Research Notices, 2002, Nr. 11, p. 573-611. arXiv: nlin.SI/0110004

49. A.I. Bobenko, T. Hoffmann, Yu.B. Suris. Hexagonal circle patterns and integrable systems: patterns with the multi-ratio property and Lax equations on the regular triangular lattice. Intern. Math. Research Notices, 2002, Nr. 3, p. 111-164. arXiv: math.CV/0104244

48. Yu.B. Suris. Integrable discretizations of some cases of the rigid body dynamics. J. Nonlin. Math. Phys., 2001, 8, p. 534-560. arXiv: nlin.SI/0105012

47. Yu.B. Suris. Integrability of Adler's discretization of the Neumann system. Phys. Lett. A, 2001, 279, p. 327-332. arXiv: nlin.SI/0005054

46. A.I. Bobenko, Yu.B. Suris. A discrete time Lagrange top and discrete elastic curves. - In: L.D. Faddeev's Seminar on Mathematical Physics, Ed. M. Semenov-Tian-Shansky. Amer. Math. Soc., 2000, p. 39-62.

45. Yu.B. Suris. A reply to a comment: a note on an integrable discretization of the nonlinear Schrödinger equation. Inverse Problems, 2000, 16, p. 1071-1077.

44. Yu.B. Suris. The motion of a rigid body in a quadratic potential: an integrable discretization. Intern. Math. Research Notices, 2000, Nr. 12, p. 643-663. arXiv: solv-int/9909009

43. A.I. Bobenko, Yu.B. Suris. Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semi-direct products. Lett. Math. Phys., 1999, 49, p. 79-93. arXiv: math.SG/9906108

42. Yu.B. Suris. R-matrices for relativistic deformations of integrable systems. J. Nonlin. Math. Phys., 1999, 6, p. 411-447. arXiv: solv-int/9906010

41. A.I. Bobenko, Yu.B. Suris. Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top. Commun. Math. Phys., 1999, 204, p. 147-188. arXiv: solv-int/9810018

40. Yu.B. Suris. Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties. Rev. Math. Phys., 1999, 11, p. 727-822. arXiv: solv-int/9709005

39. Yu.B. Suris, O. Ragnisco. What is the relativistic Volterra lattice? Commun. Math. Phys., 1999, 200, p. 445-485. arXiv: solv-int/9802016

38. Yu.B. Suris. R-matrices and integrable discretizations. - In: Discrete Integrable Geometry and Physics, Eds A. Bobenko, R. Seiler, Oxford: Clarendon Press, 1999, p. 157-207.

37. Yu.B. Suris. R-matrix hierarchies, integrable lattice systems, and their integrable discretizations. - In: Symmetries and Integrability of Difference Equations, Eds. P. Clarkson, F. Nijhoff, Cambridge Univ. Press, 1999, p. 79-94. arXiv: solv-int/9607005

36. A.I. Bobenko, B. Lorbeer, Yu.B. Suris. Integrable discretizations of the Euler top. J. Math. Phys., 1998, 39, p. 6668-6683. arXiv: solv-int/9803016

35. Yu.B. Suris. On an integrable discretization of the modified Korteweg-de Vries equation. Phys. Lett. A, 1997, 234, p. 91-102. arXiv: solv-int/9702003

34. Yu.B. Suris. A note on an integrable discretization of the nonlinear Schrödinger equation. Inverse Problems, 1997, 13, p. 1121-1136. arXiv: solv-int/9701010

33. Yu.B. Suris. Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices. J. Math. Phys., 1997, 38, p. 4179-4201. arXiv: solv-int/9610001

32. Yu.B. Suris. On some integrable systems related to the Toda lattice. J. Phys. A, 1997, 30, p. 2235-2249. arXiv: solv-int/9605010

31. Yu.B. Suris. New integrable systems related to the relativistic Toda lattice. J. Phys. A, 1997, 30, p. 1745-1761. arXiv: solv-int/9605006

30. O. Ragnisco, Yu.B. Suris. Integrable discretizations of the spin Ruijsenaars-Schneider models. J. Math. Phys., 1997, 38, p. 4680-4691. arXiv: solv-int/9605001

29. Yu.B. Suris. Why is the Ruijsenaars-Schneider hierarchy governed by the same R-operator as the Calogero-Moser one? Phys. Lett. A, 1997, 225, p. 253-262. arXiv: hep-th/9602160, solv-int/9603011

28. O. Ragnisco, Yu.B. Suris. On the r-matrix structure of the Neumann system and its discretizations. - In: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, Birkhäuser, 1996, p. 285-300.

27. Yu.B. Suris. Integrable discretizations of the Bogoyavlensky lattices. J. Math. Phys., 1996, 37, p. 3982-3996. arXiv: solv-int/9512007

26. Yu.B. Suris. Partitioned Runge-Kutta methods as phase-volume preserving integrators. Phys. Lett. A, 1996, 220, p. 63-69.

25. Yu.B. Suris. A discrete time peakons lattice. Phys. Lett. A, 1996, 217, p. 321-329. arXiv: solv-int/9512001

24. Yu.B. Suris. A discrete-time relativistic Toda lattice. J. Phys. A., 1996, 29, p. 451-465. arXiv: solv-int/9510007

23. Yu.B. Suris. Bi-Hamiltonian structure of the qd algorithm and new discretizations of the Toda lattice. Phys. Lett. A, 1995, 206, p. 153-161.

22. Yu.B. Suris. Dynamical r-matrices for some nonlinear oscillators. J. Phys. A, 1995, 28, p. L85-L90.

21. Yu.B. Suris. Discrete-time analogs of some nonlinear oscillators in an inverse-square potential. J. Phys. A, 1994, 27, p. 8161-8169.

20. Yu.B. Suris. A family of integrable standard-like maps related to symmetric spaces. Phys. Lett. A, 1994, 192, p. 9-16.

19. Yu.B. Suris. On the complex separatrices of some standard-like maps. Nonlinearity, 1994, 7, p. 1225-1236.

18. Yu.B. Suris. A discrete-time Garnier system. Phys. Lett. A, 1994, 189, p. 281-289.

17. Yu.B. Suris. On the r-matrix interpretation of Bogoyavlensky lattices. Phys. Lett. A, 1994, 188, p. 256-262.

16. Yu.B. Suris. On the bi-Hamiltonian structure of Toda and relativistic Toda lattices. Phys. Lett. A, 1993, 180, p. 419-429.

15. Yu.B. Suris. On the algebraic structure of the Bruschi-Ragnisco lattice. Phys. Lett. A, 1993, 179, p. 403-406.

14. Yu.B. Suris. Splitting of separatrices and symbolic dynamics for some degenerate standard-like maps. Physica D, 1993, 63, p. 243-272.

13. Yu.B. Suris. Algebraic structure of discrete-time and relativistic Toda lattices. Phys. Lett. A, 1991, 156, p. 467-474.

12. Yu.B. Suris. On the conservation of integral invariants in the course of numerical integration of systems $\ddot{x}=K\dot{x}+f(x)$ . USSR J. Comput. Math. and Math. Phys., 1991, 31, p. 36-44.

11. Yu.B. Suris. Discrete-time generalized Toda lattices: complete integrability and relation with relativistic Toda lattices. Phys. Lett. A, 1990, 145, p. 113-119.

10. Yu.B. Suris. Generalized Toda chains in discrete time. Leningrad Math. J., 1990, 2, p. 339-352.

9. Yu.B. Suris. Hamiltonian methods of Runge-Kutta type and their variational interpretation. Math. Modelling, 1990, 2, p. 78-87 (in Russian).

8. Yu.B. Suris. On Lyapunov irreducibility of Schroedinger equation with quasi-periodic potential. Diff. Equations, 1990, 25, p. 1362-1369.

7. Yu.B. Suris. On integrable standard-like mappings. Funct. Anal. Appl., 1989, 23, p. 74-76.

6. Yu.B. Suris. On the canonicity of mappings generated by Runge-Kutta-type methods for systems $\ddot{x}=-\partial U/\partial x$. USSR J. Comput. Math. and Math. Phys., 1989, 29, p. 138-144.

5. Yu.B. Suris. On the conservation of symplectic structure in the course of numerical integration of Hamiltonian systems. - In: Numerical solution of differential equations, Ed. S. Filippov, Moscow, Keldysh Inst. of Appl. Math., 1988, p. 148-160 (in Russian).

4. Yu.B. Suris. On some properties of methods for numerical integration of systems $\ddot{x}=f(x)$. USSR J. Comput. Math. and Math. Phys., 1987, 27, p. 149-156.

3. Yu.B. Suris. Symbolic dynamics for nonlinear nonautonomous oscillator. Diff. Uravneniya, 1987, 23, p. 535-538 (in Russian).

2. Yu.B. Suris. On the quasi-random dynamical systems generated by finite-difference approximations of completely integrable Hamiltonian systems. VINITI, Nr. 5173-B (1986), 78 pp. (in Russian).

1. Yu.V. Rakitskii, E.D. Shchukin, V.S. Yushchenko, I.A. Tsukerman, Yu.B. Suris, and A.I. Slutsker. Mechanism of the formation of energy fluctuations and a method for studying it. Sov. Phys. Chem. Doklady, 1986, 285, p. 1204-1207.