Skip to main content
Log in

Reduction of Abelian Functions and Algebraically Integrable Systems. II

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

REFERENCES

  1. H. Airault, H. P. McKean, and J. Moser, "Rational and elliptic solutions of the KdV equation and a related many-body problem," Commun. Pure Appl. Math., 30, 94-148 (1977).

    Google Scholar 

  2. G. G. Appelrott, "The simplest cases of motion of heavy asymmetric Kovalevskaya gyroscope," Mat. Sb., 27, 477-561 (1903).

    Google Scholar 

  3. Yu. Arkhangelskii, Analytical Dynamics of a Rigid Body [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  4. H. F. Baker, Abel Theorem and the Allied Theory Including the Theory of Theta Functions, Cambridge Univ. Press, Cambridge (1897).

    Google Scholar 

  5. S. Baker, V. Z. Enolskii, and A. P. Fordy, "Integrable quartic potentials and coupled KdV equations," Phys. Lett. A, 201, 167-174 (1995).

    Google Scholar 

  6. W. Barth, C. Peters, and A. Van de Ven, Compact Complex Surfaces, Springer, Berlin-Heidelberg-New York-Tokyo (1984).

    Google Scholar 

  7. V. G. Bar'yakhtar, E. D. Belokolos, and A. M. Korostil, "Superconductivity of layered systems in a finite-gap potential model," Metalofizika, 13, No. 5, 3-8 (1991).

    Google Scholar 

  8. V. G. Bar'yakhtar, E. D. Belokolos, and A. M. Korostil, "The method of separable finite-gap potentials-a new method for calculating the electron energy structure of solids," Metallofizika, 14, No. 8, 3-11 (1992).

    Google Scholar 

  9. V. G. Bar'yakhtar, E. D. Belokolos, and A. M. Korostil, "A new method for calculating the electron spectrum in solids. Application to high-temperature superconductors," Phys. Stat. Sol., 169, No. 1, 105-114 (1992).

    Google Scholar 

  10. V. G. Bar'yakhtar, E. D. Belokolos, and A. M. Korostil, "Fermi surfaces of electrons for metals with the fcc structure in the finite-gap potential model," Metallofizika, 15, No. 12, 3-13 (1993).

    Google Scholar 

  11. H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 2, McGraw-Hill, New York (1955).

    Google Scholar 

  12. E. D. Belokolos, A. I. Bobenko, V. Z. Enolskii, A. R. Its, and V. B. Matveev, Algebro-Geometrical Aproach to Nonlinear Integrable Equations, Springer, Berlin (1994).

    Google Scholar 

  13. E. D. Belokolos and V. Z. Enolskii, "On the solutions in elliptic functions of nonlinear partial differential equations, integrable by the inverse scattering method," Usp. Mat. Nauk, 37, 89 (1982).

    Google Scholar 

  14. E. D. Belokolos and V. Z. Enolskii, "On the expression of the parameters for the solution of completely integrable equations in terms of theta constants," Funkts. Anal. Prilozh., 21, No. 3, 61-62 (1987).

    Google Scholar 

  15. E. D. Belokolos and V. Z. Enolskii, "Algebraically integrable nonlinear equations and Humbert surfaces," In: Plasma Theory and Nonlinear and Turbulent Processes in Physics, Vol. 1 (V. G. Baryakhtar et al., Eds.), World Scientific, Singapore (1988).

    Google Scholar 

  16. E. D. Belokolos and V. Z. Enolskii, "Isospectral deformations of elliptic potentials," Russ. Math. Surv., 44, No. 5, 155-156 (1989).

    Google Scholar 

  17. E. D. Belokolos and V. Z. Enolskii, "Verdier elliptic solitons and Weierstrass reduction theory," Funkts. Anal. Prilozh., 23, No. 1, 75-76 (1989).

    Google Scholar 

  18. E. D. Belokolos and V. Z. Enolskii, "Reduction of theta functions and elliptic finite-gap potentials," Acta Appl. Math., 36, 87-117 (1994).

    Google Scholar 

  19. E. D. Belokolos and V. Z. Enolskii, "Reduction of Abelian functions and algebraically integrable systems, I," In: Progress in Science and Technology, Series on Contemporary Mathematics and Its Applications,The matic Surveys [in Russian], Vol. 71, All-Russian Institute for Scientific and Technical Information (VINITI), Moscow (2000), in press.

  20. E. D. Belokolos and A. M. Korostil, "Electron-phonon interaction in conductors with one-gap separable potential," Metallofizika, 13, No. 6, 3-11 (1991).

    Google Scholar 

  21. K. J. Blow, N. J. Doran, and D. Wood, "Polarization instabilities for solitons in birefringent fibers," Opt. Lett., 12, 202-204 (1987).

    Google Scholar 

  22. O. Bolza, "Ñber die Reduction hyperelliptischer Integrale erster Ordnung und erster Gattung auf elliptische durch eine Transformation vierten Grades," Math. Ann., 28, 47-496 (1887).

    Google Scholar 

  23. V. M. Buchstaber and V. Z. Enolskii, "Abelian Bloch solutions of the two-dimensional Schrödinger equation," Usp. Mat. Nauk, 50, No. 1, 191-192 (1995).

    Google Scholar 

  24. V. M. Buchstaber, V. Z. Enolskii, and D. V. Leykin, "Kleinian functions, hyperelliptic Jacobians and applications," In: Reviews in Mathematics and Mathematical Physics (S. P. Novikov and I. M. Krichever, Eds.), Vol. 10, No. 2, Gordon and Breach (1997), pp. 1-125.

  25. W. Burnside, "On the form of hyperelliptic integrals of the first order which are expressible as the sum of two elliptic integrals," Proc. London Math. Soc., 23, 173-185 (1892).

    Google Scholar 

  26. O. A. Chalykh and A. P. Veselov, "Commutative rings of partial differential operators and Lie algebras," Commun. Math. Phys, 126, 597-611 (1990).

    Google Scholar 

  27. C. A. Chaplygin, New Case of Rotation of a Rigid Body with a Fixed Point [in Russian], Gostekhizdat, Moscow (1954).

    Google Scholar 

  28. P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, "Quasi-periodic solutions of coupled nonlinear Schrödinger equations," Proc. Roy. Soc. London, A, 451, 685-700 (1995).

    Google Scholar 

  29. P. L. Christiansen, J. C. Eilbeck, V. Z. Enolskii, and N. A. Kostov, "Quasi periodic solutions of Manakov type coupled nonlinear Schrödinger equations," Proc. Roy. Soc. London, A, in press.

  30. D. N. Christodoulides," Black and white vector solitons in weakly birefringent optical fibers," Phys. Lett. A, 132, 451-452 (1988).

    Google Scholar 

  31. D. N. Christodoulides and R. I. Joseph, "Vector solitons in birefringent nonlinear dispersive media," Opt. Lett., 13, 53-55 (1988).

    Google Scholar 

  32. D. V. Chudnovski and G. V. Chudnovski, "Pole expansion of nonlinear partial differential equations," Nuovo Cim. B, 42, No. 2, 339-353 (1977).

    Google Scholar 

  33. B. Deconinck and H. Segur, Pole dynamics for elliptic solutions of the Korteweg-de Vries equation solv-int/9904001 (1999).

  34. R. Dickson, F. Gesztesy, and K. Unterkofler, "Algebro-geometric solutions of the Boussinesq hierarchy," Rev. Math. Phys., 11, 823-879 (1999).

    Google Scholar 

  35. R. Dickson, F. Gesztesy, and K. Unterkofler, "A new approach to the Boussinesq hierarchy," Math. Nachr., 198, 51-108 (1999).

    Google Scholar 

  36. R. J. Dowling, "Stability of solitary waves in a nonlinear birefringent optical fiber," Phys. Rev. A, 42, 5553-5560 (1990).

    Google Scholar 

  37. B. A. Dubrovin, "Theta functions and nonlinear equations," Russ. Math. Surv., 36, 11-80 (1981).

    Google Scholar 

  38. B. A. Dubrovin, I. M. Krichever, and S. P. Novikov, "The Schrödinger equation in a periodic field on a Riemann surface," Dokl. Akad. Nauk SSSR, 229, No. 1, 15-18 (1976).

    Google Scholar 

  39. B. A. Dubrovin and S. P. Novikov, "Periodic and quasi-periodic analogs of multisoliton solutions of the Korteweg-de Vries equation," Soviet JETF, 67, No. 6, 2131-2143 (1974).

    Google Scholar 

  40. J. C. Eilbeck and V. Z. Enolskii, "Elliptic Baker-Akhiezer functions and an application to an integrable dynamical system," J. Math. Phys., 35, No. 3, 1192-1201 (1994).

    Google Scholar 

  41. J. C. Eilbeck, V. Z. Enolskii, V. B. Kuznetsov, and D. V. Leykin, "Linear r-matrix algebra for systems separable in parabolic coordinates," Phys. Lett. A, 180, 208-214 (1993).

    Google Scholar 

  42. J. C. Eilbeck, V. Z. Enolskii, V. B. Kuznetsov, and A. V. Tsiganov, "Linear r-matrix algebra for classical separable systems," J. Phys. A, 27, 567-578 (1994).

    Google Scholar 

  43. J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, "The discrete self-trapping equation," Physica D, 16, 318-338 (1985).

    Google Scholar 

  44. V. Z. Enolskii, "On the solutions in elliptic functions of integrable nonlinear equations," Phys. Lett. A, 96, 327-330 (1983).

    Google Scholar 

  45. V. Z. Enolskii, "On the two gap Lamé potentials and elliptic solutions of the Kowalewski problem connected with them," Phys. Lett. A, 100, 463-466 (1984).

    Google Scholar 

  46. V. Z. Enolskii, "Reduction g-gap solutions of equations integrable in Riemann theta functions to lower genera," In: Proc. of the IInd Workshop on Nonlinear and Turbulent Processes in Physics, New York (1984), pp. 126-129.

  47. V. Z. Enolskii and J. C. Eilbeck, "On the two-gap locus for the elliptic Calogero-Moser model," J. Phys. A: Math. Gen., 28, 1069-1088 (1995).

    Google Scholar 

  48. V. Z. Enolskii and N. A. Kostov, "On the geometry of elliptic solitons," Acta Appl. Math., 36, 57-86 (1994).

    Google Scholar 

  49. V. Z. Enolskii and M. Salerno, "Lax reprentation for two particle dynamics split on two tori," J. Phys. A.: Math. Gen., 29, 425-431 (1996).

    Google Scholar 

  50. J. Feldman, H. Knörrer, and E. Trubowitz, "There is no two-dimensional analogue of the Lamé equation," Math. Ann., 294, 295-324 (1992).

    Google Scholar 

  51. M. Florjanczyk and R. Tremblay, "Periodic and solitary waves in bimodal optical fibers," Phys. Lett. A, 141, 34-36 (1989).

    Google Scholar 

  52. A. P. Fordy, "The Hénon-Heiles system revisited," Physica D, 52, 204-210 (1991).

    Google Scholar 

  53. A. R. Forsyth, Theory of Functions of a Complex Variable, Dover Publications, Cambridge (1965).

    Google Scholar 

  54. L. Gagnon, "Self-similar solutions for coupled systems of nonlinear Schrödinger equations," J. Phys. A, 25, 2649-2667 (1992).

    Google Scholar 

  55. L. Gavrilov and A. M. Perelomov, "On explicit solution of the Calogero-Moser system," J. Math. Phys, 40, 6339-6352 (1999).

    Google Scholar 

  56. V. Ravoson, L. Gavrilov and R. Gaboz, "Separability and the Lax pair for Hénon-Heiles system," J. Math. Phys., 34(6), 2385-2390 (1993).

    Google Scholar 

  57. F. Gesztesy and R. Weikard, "Floquet theory revisited," In: Differential Equations and Mathematical Physics. Proceedings of the International Conference. March 13-17 (Univ. of Alabama at Birmingham), (1994), pp. 67-84.

  58. F. Gesztesy and R. Weikard, "Lamé potentials and the stationary (m)KdV hierarchy," Math. Nachr., 176, 73-91 (1995).

    Google Scholar 

  59. F. Gesztesy and R. Weikard, "On Picard potentials," Differ. Int. Equations, 8, 1453-1476 (1995).

    Google Scholar 

  60. F. Gesztesy and R. Weikard, "Treibich-Verdier potentials and the stationary (m)KdV hierarchy," Math. Z., 219, 451-476 (1995).

    Google Scholar 

  61. F. Gesztesy and R. Weikard, "Picard potentials and Hill's equation on a torus," Acta Math., 176, 73-107 (1996).

    Google Scholar 

  62. F. Gesztesy and R. Weikard, "A characterization of all elliptic algebro-geometrical solutions of AKNS hierarchy," Acta Math., 181, 161-169 (1998).

    Google Scholar 

  63. F. Gesztesy and R. Weikard, "Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies-an analytic approach," Bull. Amer. Math. Soc., 35, No. 4, 271-317 (1998).

    Google Scholar 

  64. F. Gesztesy and R.Weikard, "Toward a characterization of elliptic solutions of hierarchies of soliton equations," Contemp. Math., 221, 133-161 (1999).

    Google Scholar 

  65. G. H. Halphen, "Mémoire sur la réduction des équations différentielles linéaires aux formes intégrales," Mem. Prés. l'Acad de Sci. de France, 28, 1-300 (1884).

    Google Scholar 

  66. M. Hénon and C. Heiles, "The applicability of the third integral of motion: some numerical experiments," Astrophys., 63, 73-78 (1964).

    Google Scholar 

  67. C. Hermite, Oeuvres de Charles Hermite, Vol. III, Gauthier-Villars, Paris (1912).

    Google Scholar 

  68. J. Hietarinta, "Direct method for the search of the second invariant," Phys. Rep., 147, 87-154 (1987).

    Google Scholar 

  69. E. L. Ince, "Further investigation into periodic Lamé functions," Proc. Roy. Soc. Edinburgh, 60, 83-99 (1940).

    Google Scholar 

  70. A. R. Its and V. B. Matveev, "Hill's operators with a finite number of lacunae and multisoliton solutions of the Korteweg-de Vries equation," Teor. Mat. Fiz. 23, 51-67 (1975).

    Google Scholar 

  71. M. F. Jorgensen and P. L. Christiansen, "Hamiltonian structure for a modified discrete self-trapping equation," Chaos, Solitons, and Fractals, 4, 217-225 (1994).

    Google Scholar 

  72. E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen. Vol i. Gewohnliche Differentialgleichungen, Leipzig (1959).

  73. S. Koizumi, "The equations defining Abelian varieties and modular functions," Math. Ann., 242, 127-145 (1979).

    Google Scholar 

  74. N. A. Kostov, "Quasi-periodical solutions of the integrable dynamical systems related to Hill's equation," Lett. Math. Phys., 17, 95-104 (1989).

    Google Scholar 

  75. N. A. Kostov and V. Z. Enolskii, "On the spectral characteristics of elliptic solitons," Mat. Zametki, 53(3), 62-71 (1993).

    Google Scholar 

  76. N. A. Kostov and M. Uzunov, "New kinds of periodical waves in birefringent optical fibers," Opt. Com., 89, 389-392 (1992).

    Google Scholar 

  77. S. Kowalewski, "Sur le probléme de la rotation d'un corps solide autour d'un point fixe," Acta Math., 12, 177-232 (1889).

    Google Scholar 

  78. M. Krause, Theorie der doppeltperiodischen Functionen einer veränderlichen Grösse. Vol. i, Teubner, Leipzig (1895).

    Google Scholar 

  79. A. Krazer, Lehrbuch der Thetafunktionen, Teubner, Leipzig (1903).

    Google Scholar 

  80. I. M. Krichever, "The method of algebraic geometry in the theory of nonlinear equations," Russ. Math. Surv., 32, 180-208 (1977).

    Google Scholar 

  81. I. M. Krichever, "Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable particle systems," Funkts. Anal. Prilozh., 14, 45-54 (1980).

    Google Scholar 

  82. I. M. Krichever, "Spectral theory of two dimensional periodic operators and its application," Russ. Math. Surv., 44(2), 121-184 (1989).

    Google Scholar 

  83. N. Manganaro and D. F. Parker, "Similarity reductions for variable-coefficient coupled nonlinear Schrödinger equations," J. Phys. A, 26, 4093-4106 (1993).

    Google Scholar 

  84. H. P. McKean and P. van Moerbeke, "The spectrum of Hill's operator," Invent. Math., 30, 217-274 (1975).

    Google Scholar 

  85. C. R. Menyuk, "Nonlinear pulse-propagation in birefringent optical fibers," IEEE J. Quan. Electron., 23, 174-176 (1987).

    Google Scholar 

  86. S. P. Novikov, "Periodic problem for the Korteweg-de Vries equation," Funkts. Anal. Prilozh., 74, 54-66 (1974).

    Google Scholar 

  87. S. P. Novikov, "Two-dimensional Schrödinger operators in periodic fields," In: Progress in Science and Technology, Series on Contemporary Problems in Mathematics [in Russian], Vol. 23, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1983), pp. 3-35.

    Google Scholar 

  88. A. Porubov and D. Parker, "Some general periodic solutions to coupled nonlinear Schrödinger equations," Wave Motion, 29, 97-109 (1999).

    Google Scholar 

  89. E. Previato and J. L. Verdier, "Galois-Boussinesq tangential covers," In: Proceedings of the Indo-French Conference on Geometry, Bombay 1989 (Delhi) (A. Beauville and S. Ramanan, Eds.), Hindustan Book Agency (1993).

  90. V. Ravoson, A. Ramani, and B. Gramaticos, "Generalized separability for a Hamiltonian with nonseparable quartic potential," Phys. Lett. A, 191, 91-95 (1994).

    Google Scholar 

  91. G. Rosenhain, "Abhandlung uber die Funktionen zweier Variabler mit vier Perioden," Mem. Pres. l'Acad. de Sci. de France, IX, 361-455 (1851).

    Google Scholar 

  92. R. Sahadevan, K. M. Tamizhmani, and M. Lakshmanan, "Painleve analysis and integrability of coupled non-linear Schrödinger-equations," J. Phys. A, 19, 1783-1791 (1986).

    Google Scholar 

  93. M. Salerno, V. Z. Enolskii, and D. V. Leykin, "A canonical transformation between integrable Hénon-Heiles systems," Phys. Rev. E, 49, 5897-5899 (1994).

    Google Scholar 

  94. A. M. Samsonov and V. V. Gurski, "On exact solution to the nonlinear reaction-diffusion equation," J. Phys. A, in press.

  95. A. M. Samsonov and V. V. Gurski, "Periodic and localized solutions to the nonlinear adsorption-diffusion equation," Stud. Appl. Math., in press.

  96. A. O. Smirnov, "A matrix analogue of the Appell theorem and reduction of multidimensional Riemann theta-functions," Mat. Sb., 61, 379-388 (1988).

    Google Scholar 

  97. A. O. Smirnov, "Elliptic solutions of the KdV equation," Mat. Zametki, 45, No. 6, 66-73 (1989).

    Google Scholar 

  98. A. O. Smirnov, "Finite-gap solution of the abelian Toda lattice of genus 4 and 5 in the elliptic functions," Teor. Mat. Fiz., 78, No. 1, 11-21 (1989).

    Google Scholar 

  99. A. O. Smirnov, "Real elliptic solutions of the sine-Gordon equation," Mat. Sb., 181, No. 6, 804-812 (1990).

    Google Scholar 

  100. A. O. Smirnov, "Elliptic in time solutions of the KdV equation," Teor. Mat. Fiz., 100, No. 2, 183-198 (1994).

    Google Scholar 

  101. A. O. Smirnov, "Elliptic solutions of the nonlinear Schrödinger and modified Korteweg-de Vries equations," Mat. Sb., 185, No. 8, 103-104 (1994).

    Google Scholar 

  102. A. O. Smirnov, "Finite-gap elliptic solutions of the KdV equation," Acta Appl. Math., 36, 125-166 (1994).

    Google Scholar 

  103. A. O. Smirnov, "Dirac operator with elliptic potential," Mat. Sb., 186, No. 8, 134-141 (1995).

    Google Scholar 

  104. A. O. Smirnov, "Two-gap elliptic solutions of the integrable nonlinear equations," Mat. Zametki, 58, No. 1, 86-97 (1995).

    Google Scholar 

  105. A. O. Smirnov, "Elliptic in time solution of the nonlinear Schrödinger equation," Teor. Mat. Fiz, 107, No. 2, 188-200 (1996).

    Google Scholar 

  106. A. O. Smirnov, "On some set of elliptic solutions of the Boussinesq equation," Teor. Mat. Fiz 109, No. 3, 347-356 (1996).

    Google Scholar 

  107. A. O. Smirnov, "Real elliptic solutions of equations connected with the 'sine'-Gordon equation," Algebra Analiz, 8, No. 3, 196-211 (1996).

    Google Scholar 

  108. A. O. Smirnov, "3-elliptic solutions of the 'sine'-Gordon equation," Mat. Zametki, 62, No. 3, 440 (1997).

    Google Scholar 

  109. A. O. Smirnov, "On some set of elliptic potentials of the Dirac operator," Mat. Sb., 188, No. 1, 109-128 (1997).

    Google Scholar 

  110. C. Sophochleous, "Symmetries for certain coupled nonlinear Schrödinger equations," J. Phys. A, 27, L515-L520 (1994).

    Google Scholar 

  111. W. R. Thickstun, "A system of particles equivalent to solitons," J. Math. Anal. Appl., 22, No. 2, 335-346 (1976).

    Google Scholar 

  112. M. V. Tratnik and J. E. Sipe, "Bound solitary waves in a birefringent optical fir," Phys. Rev. A, 38, 2011-2017 (1988).

    Google Scholar 

  113. A. Treibich, "Tangential polynomials and elliptic solitons," Duke Math. J., 59, No. 3, 611-627 (1989).

    Google Scholar 

  114. A. Treibich, "Compactified Jacobians of tangential covers, integrable systems," In: The Verdier Memorial Conference (Boston), (O. Babelon, P. Cartier, and Y. Kosmann-Schwarzbach, Eds.), Birkhäuser (1993), pp. 39-60.

  115. A. Treibich, "New elliptic potentials," Acta Appl. Math., 36, 27-48 (1994).

    Google Scholar 

  116. A. Treibich, "Matrix elliptic solitons," Duke Math. J., 90, No. 3, 523-547 (1997).

    Google Scholar 

  117. A. Treibich and J. L. Verdier, "Revêtements tangentiels et sommes de 4 nombres triangulaires," C. R. Acad. Sci.,Ser. 1, 311, 51-54 (1990).

    Google Scholar 

  118. A. Treibich and J. L. Verdier, "Solitons elliptiques," In: Grothendieck Festschrift, Volume III (Basel) (P. Cartier, L. Illusie, N. M. Katz, Y. Manin, G. Laumon, and K. A. Ribet, Eds.), Birkhäuser (1990), with an appendix by J. Oesterlé, pp. 437-480.

  119. A. Treibich and J. L. Verdier, "Revêtements exceptionnels et sommes de 4 nombres triangulaires," Duke Math. J., 68, No. 2, 217-236 (1992).

    Google Scholar 

  120. K. Unterkofler, "On the solutions of Halphen's equation," Differ. Integral Equations, (2000).

  121. G. van der Geer, "On the geometry of a Siegel modular threefold," Math. Ann., 260, 317-350 (1982).

    Google Scholar 

  122. P. Vanhaecke, "Linearising two dimensional integrable systems and the construction of action-angle variables," Math. Z., 211, 2385-2393 (1992).

    Google Scholar 

  123. J. L. Verdier, "New elliptic solitons," In: Algebraic Analysis, Special volume for the 60th Anniver. of Prof. M. Sato (M. Kashiwara and T. Kawai, Eds.), Academic Press, New York (1990), pp. 901-910.

    Google Scholar 

  124. A. P. Veselov and S. P. Novikov, "Finite zone two dimensional periodic Schrödinger operators: case of potential," Dokl. Akad. Nauk SSSR, 279, No. 4, 784-788 (1984).

    Google Scholar 

  125. A. P. Veselov and S. P. Novikov, "Finite zone two-dimensional periodic Schrödinger operators: explicit formulas and evolution equations," Dokl. Akad. Nauk SSSR, 279, No. 1, 20-24 (1984).

    Google Scholar 

  126. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, CUP, Cambridge (1973).

    Google Scholar 

  127. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Soliton Theory: Inverse Scattering Method [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  128. V. E. Zakharov and E. I. Schulman, "On the integrability of the system of 2-coupled nonlinear Schrödinger equations," Physica D, 4, 270-274 (1982).

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belokolos, E.D., Enolskii, V.Z. Reduction of Abelian Functions and Algebraically Integrable Systems. II. Journal of Mathematical Sciences 108, 295–374 (2002). https://doi.org/10.1023/A:1012800600273

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012800600273

Keywords

Navigation