Theoretical and Mathematical Physics

, Volume 99, Issue 3, pp 783–789 | Cite as

Discrete symmetries and solitons

  • A. Shabat


Soliton Discrete Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Darboux, Théorie generale des surfaces, II, Chelsea, New York, 1972.Google Scholar
  2. [2]
    A.N. Leznov, A.B. Shabat, and R.I. Yamilov, Canonical transformations generated by shifts in nonlinear lattices, Phys. Lett. A,174, (1993).Google Scholar
  3. [3]
    J. Liouville, Note sur l'integration des equations de la dynamice, J. Math. Pures Appl.20, 137–138 (1855).Google Scholar
  4. [4]
    Dubrovin B.A., Matveev V.B., and Novikov S.P., Nonlinear equations of KdV type, finite-zone linear operators and abelian varieties, Usp. Mat. Nauk.,31, No. 1, 55–136 (1976).Google Scholar
  5. [5]
    A.P. Veselov and A.B. Shabat, Dressing chain and the spectral theory of the Schrödinger operator, Funkts. Anal. i Ego Pril.,27, No. 2, 1–21 (1993).Google Scholar
  6. [6]
    V.E. Adler, Recuttings of polygons, Funkts. Anal. i Ego Pril.,27, No. 2, 79–82 (1993).Google Scholar
  7. [7]
    J.L. Burchnall and T.W. Chaundy, Commutative ordinary differential operators, Proc. London Soc. Ser. 221, 420–440 (1923).Google Scholar
  8. [8]
    A.B. Shabat, The infinite-dimensional dressing dynamical system, Inverse Problems,6, 303–308 (1992).Google Scholar
  9. [9]
    A.B. Shabat and R.I. Yamilov, Symmetries of the nonlinear chains, Leningrad Math. J.,2, No. 2, 377–400 (1991).Google Scholar
  10. [10]
    J. Weiss, Periodic fixed points of Bäcklund transformations and the KdV equation, J. Math. Phys.,27(11), 2647–2656 (1986);28(9), 2025–2039 (1987).Google Scholar
  11. [11]
    L. Infeld and T. Hull, The factorization method, Rev. Mod. Phys.,23, 21–68 (1951).Google Scholar
  12. [12]
    A. Degasperis and A. Shabat, Construction of reflectionless potentials with infinite discrete spectrum, Teor. Mat. Fiz., to appear.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. Shabat

There are no affiliations available

Personalised recommendations