Theoretical and Mathematical Physics

, Volume 142, Issue 1, pp 1–7 | Cite as

The rapidly decreasing solution of the cauchy problem for the toda lattice

  • A. Kh. Khanmamedov


We prove the existence of a rapidly decreasing solution of the Cauchy problem for the Toda lattice. We find a class of initial data guaranteeing the existence of such a solution.


Toda lattice rapidly decreasing solution scattering data 


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  1. 1.
    H. Flashka, Progr. Theoret. Phys., 51, 703–716 (1974).Google Scholar
  2. 2.
    S. V. Manakov, JETP, 40, 269–274 (1975).Google Scholar
  3. 3.
    V. A. Marchenko, Sturm-Liouville Operators and Their Applications[in Russian], Naukova Dumka, Kiev (1977); English transl., Birkh¨auser, Basel (1986).Google Scholar
  4. 4.
    L. A. Takhtadzhyan and L. D. Faddeev, Hamiltonian Approach to the Theory of Solitons [in Russian], Nauka, Moscow (1986); English transl.: L. D. Faddeev and L. A. Takhtajan The Hamiltonian Methods in the Theory of Solitons, Berlin, Springer (1987).Google Scholar
  5. 5.
    M. Toda, Nonlinear Lattice Dynamics[in Japanese], Iwanami Shoten, Tokyo (1978); English transl.: Theory of Nonlinear Lattices, Springer, Berlin (1981).Google Scholar
  6. 6.
    I. M. Guseinov and A. Kh. Khanmamedov, Theor. Math. Phys., 119, 739–749 (1999).Google Scholar
  7. 7.
    G. Sh. Guseinov, Sov. Math. Dokl., 17, 1684–1688 (1977).Google Scholar
  8. 8.
    G. Sh. Guseinov, “Inverse scattering transform for self adjoint second-order differential operators,” Candidate’s dissertation, Moscow State Univ., Moscow (1976).Google Scholar
  9. 9.
    S. G. Krein, Linear Differential Equations in Banach Space[in Russian], Nauka, Moscow (1969); English transl., Amer. Math. Soc., New York (1972).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. Kh. Khanmamedov
    • 1
  1. 1.Baku State UniversityBaku, Azerbaijan

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