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Explicit Bäcklund transformations for multifield Schrödinger equations. Jordan generalizations of the Toda chain

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Abstract

Bäcklund transformations for multifield analogs of the nonlinear Schrödinger equation that correspond to unital Jordan algebras are found. These Bäcklund transformations are explicit invertible autotransformations and as a result they are very convenient for the construction of exact solutions. It is established that to these Bäcklund transformations there correspond integrable multifield discrete—differential equations that generalize the infinite Toda chain. A simple construction is given by means of which multifield analogs of the infinite Toda chain can be constructed from every unital Jordan algebra. New examples of such chains are given.

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References

  1. A. B. Shabat and R. I. Yamilov,Algebra i Analiz,2, 183 (1990).

    Google Scholar 

  2. A. N. Leznov, A. B. Shabat, and R. I. Yamilov,Phys. Lett. A,174, 397 (1993).

    Google Scholar 

  3. A. N. Leznov, “Bäcklund transformation for integrable systems,” Preprint IHEP 92-87, Institute of High Energy Physics, Protvino (1992).

    Google Scholar 

  4. A. P. Fordy and P. Kulish,Commun. Math. Phys.,89, 427 (1983).

    Google Scholar 

  5. S. I. Svinolupov,Commun. Math. Phys.,143, 559 (1992).

    Google Scholar 

  6. C. V. Manakov,Zh. Eksp. Teor. Fiz.,65, 505 (1973).

    Google Scholar 

  7. M. Koecher,Jordan Algebras and Their Applications, Lecture Notes: University of Minnesota (1969).

  8. N. Jacobson,Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ. Vol. 39, Providence, R.I. (1968).

  9. K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov,Nearly Associative Rings [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  10. O. Loos,Jordan Pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin (1975).

    Google Scholar 

  11. S. I. Svinolupov and R. I. Yamilov,Phys. Lett. A,160, 548 (1991).

    Google Scholar 

  12. A. V. Shabat and R. I. Yamilov,Phys. Lett. A,130, 271 (1988).

    Google Scholar 

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Authors
  1. S. I. Svinolupov
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  2. R. I. Yamilov
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Additional information

Institute of Mathematics, Ural Scientific Center, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 2, pp. 207–219, February, 1994.

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Svinolupov, S.I., Yamilov, R.I. Explicit Bäcklund transformations for multifield Schrödinger equations. Jordan generalizations of the Toda chain. Theor Math Phys 98, 139–146 (1994). https://doi.org/10.1007/BF01015792

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  • DOI: https://doi.org/10.1007/BF01015792

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