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Integrability conditions for systems of two equations of the form u t =A(u)u xx +F(u, u x ). I

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Literature Cited

  1. M. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981).

    Google Scholar 

  2. V. V. Sokolov and A. B. Shabat, Sov. Sci. Rev. C,4, 221 (1984).

    Google Scholar 

  3. F. B. Estabrook and H. D. Wahlquist, J. Math. Phys.,16, 1 (1975).

    Google Scholar 

  4. F. B. Estabrook and H. D. Wahlquist, J. Math. Phys.,17, 1293 (1976).

    Google Scholar 

  5. N. Kh. Ibragimov and A. B. Shabat, Funktsional. Analiz i Ego Prilozhen.,14, 79 (1980).

    Google Scholar 

  6. V. V. Golubev, Lectures on the Mathematical Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  7. A. V. Zhiber, and A. B. Shabat, Dokl. Akad. Nauk SSSR,247 1103 (1979).

    Google Scholar 

  8. S. I. Svinolupov and V. V. Sokolov, Funktsional. Analiz i Ego Prilozhen.,16, 86 (1982).

    Google Scholar 

  9. R. I. Yamilov, Usp. Mat. Nauk,38, 155 (1983).

    Google Scholar 

  10. P. D. Lax, Commun. Pure Appl. Math.,21, 467 (1968).

    Google Scholar 

  11. F. Magri, J. Math. Phys.,19, 1156 (1978).

    Google Scholar 

  12. V. E. Zakharov and E. P. Schulman, Physica (Utrecht),4D, 270 (1982).

    Google Scholar 

  13. A. P. Fordi and P. P. Kulish, Commun. Math. Phys.,89, 427 (1983).

    Google Scholar 

  14. E. K. Sklvanin, “On complete integrability of the Landau-Lifshitz equation,” Preprint E-3-1979 [in English], LOMI, Leningrad (1979).

    Google Scholar 

  15. M. Wadati, K. Konno, and Y. H. Ichikawa, J. Phys. Soc. Jpn.,47, 1968 (1979).

    Google Scholar 

  16. I. M. Gel'fand and L. A. Dikii, Funktsional. Analiz i Ego Prilozhen.,10, 13 (1976).

    Google Scholar 

  17. Yu. I. Manin, Modern Problems of Mathematics, Vol. 11 [in Russian], VINITI, Moscow (1978), pp. 5–152.

    Google Scholar 

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Authors
  1. A. V. Mikhailov
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  2. A. B. Shabat
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Additional information

L. D. Landau Institute of Theoretical Physics, USSR Academy of Sciences; Department of Physics and Mathematics with Computational Center, Bashkir Branch, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 62, No. 2, pp. 163–185, February, 1985.

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Mikhailov, A.V., Shabat, A.B. Integrability conditions for systems of two equations of the form u t =A(u)u xx +F(u, u x ). I. Theor Math Phys 62, 107–122 (1985). https://doi.org/10.1007/BF01033520

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  • DOI: https://doi.org/10.1007/BF01033520

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