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Prog. Theor. Phys. Vol. 51 No. 3 (1974) pp. 703-716
On the Toda Lattice. II
— Inverse-Scattering Solution
—
H. Flaschka
Department of Mathematics, The University of Arizona, Tucson, Arizona 85721
(Received September 17, 1973)
Abstract:
An inverse-scattering method is developed for the solution of the exponential lattice of Toda. As application of this method, the general N-soliton formula is derived, and constants of the motion are expressed in terms of the scattering data.
URL :
http://ptp.ipap.jp/link?PTP/51/703/
DOI : 10.1143/PTP.51.703
References:
- M. Toda, Prog. Theor. Phys. Suppl. No. 45 (1970), 174[PTP].
-
M. Toda, J. Phys. Soc. Jpn. 22 (1967), 431[JPSJ];
ibid. 23 (1967), 501[JPSJ].
- J. Ford, S. D. Stoddard and J. S. Turner, Prog. Theor. Phys., to appear.
- M. Hènon, to appear in Phys. Rev.
- H. Flaschka, to appear in Phys. Rev.
-
M. Toda and M. Wadati, J. Phys. Soc. Jpn. 34 (1973), 18[JPSJ].
-
C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Phys. Rev. Lett. 19 (1967), 1095[APS].
- V. E. Zakharov and L. D. Faddeev, Funk. Anal. i evo Priloz. 5 (1971), 18.
-
M. Wadati, J. Phys. Soc. Jpn. 34 (1973), 1289[JPSJ].
- V. E. Zakharov and A. B. Shabat, Sov. Phys. -JETP 34 (1972), 62.
-
M. J. Ablowitz, D. J. Kaup, A. C. Newell and H. Segur, Phys. Rev. Lett. 30 (1973), 1262[APS];
ibid. 31 (1973), 125[APS].
-
R. Hirota, J. Phys. Soc. Jpn. 35 (1973), 286[JPSJ].
-
K. M. Case and M. Kac, J. Math. Phys. 14 (1973), 594[CrossRef].
-
K. M. Case, J. Math. Phys. 14 (1973), 916[CrossRef].
- L. D. Faddeev, Am. Math. Soc. Translations 65 (1967), 139.
- P. D. Lax, Comm. Pure Appl. Math 21 (1968), 467.
- For a detailed account of the spectral theory of difference operators, see Ju. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators, AMS Transl. of Math. Monographs, v. 17, Providence, R. I. 1968.
- V. de Alfaro and T. Regge, Potential Scattering (North-Holland, Amsterdam 1965).
- I. M. Gel'fand and B. M. Levitan, Am. Math. Soc. Translations 1 (1955), 253.
- Z. S. Agranovic and V. A. Marčenko, The Inverse Problem of Scattering Theory (Gordon and Breach, New York, 1963).
-
M. J. Ablowitz and A. C. Newell, J. Math. Phys. 14 (1973), 1277[CrossRef].
-
M. Wadati and M. Toda, J. Phys. Soc. Jpn. 32 (1972), 1403[JPSJ].
- V. S. Buslaev and L. D. Faddeev, DAN 132 (1960), 13.
- I. C. Percival, Proc. Phys. Soc. 80 (1962), 1290.
- V. S. Buslaev, Topics in Mathematical Physics, ed. M. Sh. Birman, v.l, (Leningrad 1966. Engl. Transl. Plenum Press, 1967).
- I. M. Gel'fand and N. Ja, Vilenkin, Generalized Functions, v. 4, (Academic Press, New York, 1965).
- A. I. Markushevich, Theory of Functions of a Complex Variable, v. 2, (Prentice-Hall, Englewood Cliffs, N. J. 1965).
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