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Integrable Deformations of Algebraic Curves

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We present a general scheme for determining and studying integrable deformations of algebraic curves, based on the use of Lenard relations. We emphasize the use of several types of dynamical variables: branches, power sums, and potentials.

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REFERENCES

  1. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984); E. D. Belokolos, A. I. Bobenko, V. Z. Enolski, A. R. Its, and V. B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer, Berlin (1994); B. A. Dubrovin and S. P. Novikov, Russ. Math. Surveys, 44, No. 6, 35 (1989); H. Flaschka, M. G. Forest, and D. W. Mclauglin, Comm. Pure Appl. Math., 33, 739 (1980); B. A. Dubrovin, Comm. Math. Phys., 145, 415 (1992).

    Google Scholar 

  2. I. M. Krichever, Funct. Anal. Appl., 22, 200 (1988); Comm. Pure Appl. Math., 47, 437 (1994).

    Article  Google Scholar 

  3. Y. Kodama and B. G. Konopelchenko, J. Phys. A, 35, L489–L500 (2002); “Deformations of plane algebraic curves and integrable systems of hydrodynamic type,” in: Nonlinear Physics: Theory and Experiment II (Proc. Intl. Workshop, Gallipoli, Lecce, Italy, 2002, M. J. Ablowitz, M. Boiti, F. Pempinelli, and B. Prinari, eds.), World Scientific, River Edge, N. J. (2003), p. 234.

    Google Scholar 

  4. B. G. Konopelchenko and L. Martinez Alonso, J. Phys. A, 37, 7859 (2004).

    Google Scholar 

  5. C. L. Siegel, Topics in Complex Function Theory, Vol. 1, Elliptic Functions and Uniformization Theory, Wiley, New York (1969).

    Google Scholar 

  6. R. Y. Walker, Algebraic Curves, Springer, Berlin (1978).

    Google Scholar 

  7. S. S. Abhyankar, Algebraic Geometry for Scientists and Engineers (Math. Surveys and Monographs, Vol. 35), Amer. Math. Soc., Providence, R. I. (1990).

    Google Scholar 

  8. B. L. van der Waerden, Algebra, Vol. 1, Springer, Berlin (1991).

    Google Scholar 

  9. L. Redei, Introduction to Algebra, Vol. 1, Pergamon, Oxford (1967).

    Google Scholar 

  10. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon, Oxford (1979).

    Google Scholar 

  11. L. Schwartz, Analyse mathematique, Vol. 2, Hermann, Paris (1967).

    Google Scholar 

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 94–101, July, 2005.

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Kodama, Y., Konopelchenko, B.G. & Martinez Alonso, L. Integrable Deformations of Algebraic Curves. Theor Math Phys 144, 961–967 (2005). https://doi.org/10.1007/s11232-005-0123-9

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