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Solitons and magnons in the classical heisenberg chain

Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 131)

Keywords

Solitary Wave Poisson Bracket Spin Wave Canonical Variable Solitary Wave Solution 
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.

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List of references

  1. 1.
    J.B. Torrance, Jr., and M. Tinkham, Phys. Rev. 187, 587 (1969)CrossRefGoogle Scholar
  2. 2.
    J.B. Torrance, Jr., and M. Tinkham, Phys. Rev. 187, 595 (1969)CrossRefGoogle Scholar
  3. 3.
    D.F. Nicoli and M. Tinkham, Phys. Rev. B9, 3126 (1974)Google Scholar
  4. 4.
    H.C. Fogedby, Phys. Rev. B5, 1941 (1972)Google Scholar
  5. 5.
    H.C. Fogedby and H. Højgaard Jensen, Phys. Rev. B6, 3444 (1972)Google Scholar
  6. 6.
    H.C. Fogedby, Phys. Rev. B8, 2200 (1973)Google Scholar
  7. 7.
    H.C. Fogedby, Phys. Rev. B10, 4000 (1974)Google Scholar
  8. 8.
    L.D. Landau and E.M. Lifschitz, Quantum Mechancis (Pergamon, London 1958)Google Scholar
  9. 9.
    E. Ising, Z. Phys. 31, 253 (1925)Google Scholar
  10. 10.
    H.A. Bethe, Z. Phys. 71, 205 (1931)CrossRefGoogle Scholar
  11. 11.
    F. Bloch, Z. Phys. 61, 206 (1930)CrossRefGoogle Scholar
  12. 12.
    C. Kittel, Introduction to Solid State Physics (Wiley, London 1971)Google Scholar
  13. 13.
    R. Orbach, Phys. Rev. 112, 309 (1958)CrossRefGoogle Scholar
  14. 14.
    M. Wortis, Phys.Rev. 132, 85 (1963)CrossRefGoogle Scholar
  15. 15.
    J. Hanus, Phys. Rev. Lett. 11, 336 (1963)CrossRefGoogle Scholar
  16. 16.
    J.E. van Himbergen and J.A. Tjon, Physica 76, 503 (1974)CrossRefGoogle Scholar
  17. 17.
    R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, New York 1966)Google Scholar
  18. 18.
    E. Janhke and F. Emde, Tables of Functions with Formulae and Curves (Dover, New York, 1945)Google Scholar
  19. 19.
    H. Højgaard Jensen (private communication)Google Scholar
  20. 20.
    P.C. Martin, Houches Lectures, 1967; edited by C.N. DeWitt and R. Balian (Gordon and Breach, New York 1967)Google Scholar
  21. 21.
    D. Forster, Hydrodynamic Fluctuations. Broken Symmetry and Correlation Functions (Benjamin, Reading, Mass. USA 1975)Google Scholar
  22. 22.
    J.B. Torrance, Jr., Ph.D. thesis (Harvard University, 1968) (unpublished); Harvard University, Division of Engineering and Applied Physics, Technical Report No. 1, 1969 (unpublished)Google Scholar
  23. 23.
    H.C. Fogedby, unpublishedGoogle Scholar
  24. 24.
    A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Pergamon, Oxford 1965)Google Scholar
  25. 25.
    N.N. Bogoliubov and D.V. Shirkov, Introduction to the Theory of Quantised Fields (Interscience, New York 1959)Google Scholar
  26. 26.
    H.C. Fogedby, J.Phys. C11, 2801 (1978)Google Scholar
  27. 27.
    S.A. Pikin and V.M. Tsukernik, Sov. Phys.-JETP 23, 914 (1965)Google Scholar
  28. 28.
    P. Pfeuty, Ann. Phys. (N.Y.) 57, 79 (1970)CrossRefGoogle Scholar
  29. 29.
    T.N. Tommet and D.L. Huber, Phys. Rev. B11, 450 (1975)Google Scholar
  30. 30.
    P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928)CrossRefGoogle Scholar
  31. 31.
    E. Lieb, T. Schultz, and D. Mattis, Ann.Phys. (N.Y.) 16, 407 (1961)CrossRefGoogle Scholar
  32. 32.
    R. Jullien, P. Pfeuty, J.N. Fields, and S. Doniach, Phys. Rev. B18, 3568 (1978)Google Scholar
  33. 33.
    N.N. Lebedev, Special Functions and their Applications (Dover, New York 1972)Google Scholar
  34. 34.
    B. Southern and F.D.M. Haldane (private communication)Google Scholar
  35. 35.
    G. Toulouse and P. Pfeuty, Introduction au Groupe de Renormalisation et a ses Applications (Presses Universitaires, Grenoble 1975)Google Scholar
  36. 36.
    S-k. Ma, Modern Theory of Critical Phenomena (Benjamin, Reading, Mass. USA 1976)Google Scholar
  37. 37.
    H.C. Fogedby, J. Phys. C11, 4767 (1978)Google Scholar
  38. 38.
    H.C. Fogedby, J. Phys. C9, 3757 (1976)Google Scholar
  39. 39.
    H.C. Fogedby, J. Phys. C11, 2869 (1977)Google Scholar
  40. 40.
    H.C. Fogedby, J. Phys. C11, 969 (1978)Google Scholar
  41. 41.
    B.M McCoy, Phys. Rev. 173, 531 (1968)CrossRefGoogle Scholar
  42. 42.
    Th. Niemeyer, Physica 36, 377 (1967)CrossRefGoogle Scholar
  43. 43.
    B.M. McCoy, E. Barouch, and D.B. Abraham, Phys. Rev. A4, 2331 (1974)Google Scholar
  44. 44.
    S. Katsura, Phys. Rev. 127, 1508 (1962)CrossRefGoogle Scholar
  45. 45.
    B. Sutherland, J. Math. Phys. 11, 3183 (1970)CrossRefGoogle Scholar
  46. 46.
    R.J. Baxter, Phys. Rev. Lett. 26, 832 (1971); Ann. Phys. (N.Y.) 70, 193 (1972)CrossRefGoogle Scholar
  47. 47.
    J.D. Johnson, J. Krinsky, and B.M. McCoy, Phys. Rev. A8, 2526 (1973)Google Scholar
  48. 48.
    B.M. McCoy and T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambrdige, Mass. 1973)Google Scholar
  49. 49.
    A. Luther and I. Peschel, Phys. Rev. B12, 3908 (1975)Google Scholar
  50. 50.
    A. Luther and I. Peschel, Phys. Rev. B9, 2911 (1974)Google Scholar
  51. 51.
    J.M Luttinger, J. Math. 4, 1154 (1963)CrossRefGoogle Scholar
  52. 52.
    S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950)Google Scholar
  53. 53.
    P.A. Wolff, Phys. Rev. 124, 1030 (1961)CrossRefGoogle Scholar
  54. 54.
    P.C. Martin and Schwinger, Phys. Rev. 115, 1342 (1959)CrossRefGoogle Scholar
  55. 55.
    L.P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York 1962)Google Scholar
  56. 56.
    M. Wortis, Ph.D. thesis (Harvard University, 1963) (unpublished)Google Scholar
  57. 57.
    T. Holstein and H. Primakoff, Phys. Rev. 58, 1098 (1940)CrossRefGoogle Scholar
  58. 58.
    D.C. Mattis and E.H. Lieb, J. Math. Phys. 6, 304 (1965)CrossRefGoogle Scholar
  59. 59.
    A. Theumann, J. Math. Phys. 8, 2460 (1967)CrossRefGoogle Scholar
  60. 60.
    C.B. Dover, Ann. Phys. (N.Y.) 50, 500 (1968)CrossRefGoogle Scholar
  61. 61.
    R.L. Statonovich, Sov. Phys. Dokl. 2, 416 (1957)Google Scholar
  62. 62.
    J. Hubbard, Phys. Rev. Lett. 3, 77 (1959)CrossRefGoogle Scholar
  63. 63.
    J. Des Cloiseaux and J.J. Pearson, Phys. Rev. 128, 2131 (1962)CrossRefGoogle Scholar
  64. 64.
    M. Steiner, J. Villain, and C.G. Windsor, Adv. Phys. 25, 87 (1976)Google Scholar
  65. 65.
    H.C. Fogedby and A.P. Young, J. Phys. C11, 527 (1978)Google Scholar
  66. 66.
    L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, London 1959)Google Scholar
  67. 67.
    L.P. Kadanoff and P.C. Martin, Ann. Phys. (N.Y.) 24, 419 (1963)CrossRefGoogle Scholar
  68. 68.
    L.D. Landau and E.M. Lifshitz, Mechanics (Pergamon, London 1960)Google Scholar
  69. 69.
    B.I. Haperin, P.C. Hohenberg, and S-k-Ma, Phys. Rev. B10, 139 (1974)Google Scholar
  70. 70.
    P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)CrossRefGoogle Scholar
  71. 71.
    L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon, London 1959)Google Scholar
  72. 72.
    R.L. Stratonovich, Topics in the Theory of Random Noise, Vol. 1 (Gordon and Breach, New York 1963)Google Scholar
  73. 73.
    R. Graham and H. Haken, Z. Phys. 243, 289 (1971)CrossRefGoogle Scholar
  74. 74.
    R. Graham and H. Haken, Z. Phys. 243, 141 (1971)Google Scholar
  75. 75.
    S-k. Ma and G.F. Mazenko, Phys. Rev. B11, 4077 (1975)Google Scholar
  76. 76.
    L. Sasvari and P. Szepfalusy, Physica 87A, 1 (1977)Google Scholar
  77. 77.
    Y. Pomeau and P. Resiboś, Phys. Rev. C19, 64 (1975)Google Scholar
  78. 78.
    M. Månson, J. Phys. F7, 4073 (1974)Google Scholar
  79. 79.
    P. Borckmans, G. Dewel and D. Walgraef, Physica 88A, 261 (1977)Google Scholar
  80. 80.
    D. Forster, D.R. Nelson, and M.J. Stephen, Phys. Rev. Lett. 36, 867 (1976)CrossRefGoogle Scholar
  81. 81.
    D. Forster, D.R. Nelson, and M.J. Stephen, Phys. Rev. A16, 732 (1977)Google Scholar
  82. 82.
    A.M. Polyakov, Phys. Lett. B59, 79 (1975)Google Scholar
  83. 83.
    A.R. Migdal, Sov. Phys.-JETP 42, 743 (1976)Google Scholar
  84. 84.
    E. Brézin and J. Zinn-Justin, Phys. Rev. Lett. 36, 691 (1976)CrossRefGoogle Scholar
  85. 85.
    E. Brézin and J. Zinn.Justin, Phys. Rev. B14, 3110 (1976)Google Scholar
  86. 86.
    D.S. Amit and S-k-Ma (unpublished)Google Scholar
  87. 87.
    D.R. Nelson and D.S. Fisher, Phys. Rev. B16, 4945 (1977)Google Scholar
  88. 88.
    H.C. Fogedby, J. Phys. A13, 1467 (1980)Google Scholar
  89. 89.
    A.C. Scott, F.Y.F. Chu, and D.W. McLaughlin, Proceed. IEEE. 61, 1443 (1973)Google Scholar
  90. 90.
    Solitons and Condensed Platter Physics, edited by A.R. Bishóp and T. Schneider (Springer, Berlin 1979)Google Scholar
  91. 91.
    L.D. Landau and E.M. Lifshitz, Phys. Z. Sowjet 8, 153 (1935)Google Scholar
  92. 92.
    W. Döring, Z. Phys. 124, 501 (1947)Google Scholar
  93. 93.
    N.D. Mermin, J. Math. Phys. 8, 1061 (1967)CrossRefGoogle Scholar
  94. 94.
    N.D. Mermin, Phys. Rev. 134, A112 (1964)CrossRefGoogle Scholar
  95. 95.
    J. Tjon and J. Wright, Phys. Rev. B15, 3470 (1977)Google Scholar
  96. 96.
    E.T. Whittaker and G.N. Watson, A Course of Modern Analysis (University Press, Cambridge 1962)Google Scholar
  97. 97.
    H. Jeffreys and B. Jeffereys, Methods of Mathematical Physics (University Press, Cambridge 1972)Google Scholar
  98. 98.
    M. Lakshmanan, Th. W. Ruijgrok, and C.J. Thompson, Physica 84A, 577 (1976)Google Scholar
  99. 99.
    K. Nakamura and T. Sasada, Phys. Lett. 48A, 321 (1974)Google Scholar
  100. 100.
    G.B. Whitham, Linear and Non Linear Waves, (Wiley & Sons, New York 1974)Google Scholar
  101. 101.
    L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields, (Pergamon, London 1962)Google Scholar
  102. 102.
    L.A. Takhtajan, Phys. Lett. 64A, 235 (1977)Google Scholar
  103. 103.
    C.S. Gardner, J.M. Green, M.D. Kruskal, and R.M. Miura, Phys. Rev. Lett. 19, 1095 (1967)CrossRefGoogle Scholar
  104. 104.
    P.D. Lax, Commun. Pure Appl. Math. 21, 467 (1968)Google Scholar
  105. 105.
    V.E.Zakharov and A.B. Shabat, Sov. Phys.-JETP 34, 62 (1972)Google Scholar
  106. 106.
    M.J. Ablowitz, D.J. Kaup, A.C. Newell, and H. Segur, Phys. Rev. Lett. 30, (1973)Google Scholar
  107. 107.
    L.D. Faddeev, J. Math. Phys. 4, 72 (1963)CrossRefGoogle Scholar
  108. 108.
    E. Goursat, A Course in Mathematical Analysis (Dover, New York 1964)Google Scholar
  109. 109.
    G.L. Lamb Jr., Phys. Rev. Lett. 37, 235 (1976)CrossRefGoogle Scholar
  110. 110.
    G.L. Lamb Jr., J. Math. Phys. 18, 1654 (1977)CrossRefGoogle Scholar
  111. 111.
    M. Lakshmanan, Phys. Lett. 61A, 53 (1977)Google Scholar
  112. 112.
    V.E. Zakharov and S.V. Manakov, Theor. Math. Phys. 19, 551 (1975)CrossRefGoogle Scholar
  113. 113.
    L.A. Takhtajan and L.D. Faddeev, Theor. Math. Phys. 21, 1046 (1975)CrossRefGoogle Scholar
  114. 114.
    H.C. Fogedby, Physica Scripta (to be published)Google Scholar
  115. 115.
    V.E. Zakharov and L.D. Faddeev, Funct. Anal. Appl. 5, 280 (1972)CrossRefGoogle Scholar
  116. 116.
    E.L. Ince, Ordinary Differential Equations (Dover, New York 1956)Google Scholar
  117. 117.
    V.E. Korenpin and L.D. Faddeev, Theor. Math. Phys. 25, 1039 (1976)CrossRefGoogle Scholar
  118. 118.
    H.C. Fogedby, J. Phys. C13, L195 (1980)Google Scholar
  119. 119.
    A. Jevicki and M. Papanicolaou, Ann. Phys. (N.Y.) 120, 107 (1979)CrossRefGoogle Scholar
  120. 120.
    P.P. Kulish and E.K. Sklyanin, Phys.Lett. 70A, 461 (1979).Google Scholar
  121. 121.
    K.A. Long and A.P. Bishop, J. Phys. A.12, 1325 (1979)Google Scholar
  122. 122.
    V.E. Zakharov and L.A. Takhtajan, Theor. Mat. Phys. 38, 17 (1979)CrossRefGoogle Scholar

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