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On the use of closed non-Abelian prolongation algebras to find Bäcklund transformations of nonlinear evolution equations

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Lettere al Nuovo Cimento (1971-1985)

Summary

We describe a simple method to find Bäcklund transformations of a given nonlinear evolution equation, exploiting the closed non-Abelian prolongation algebra related to the equation, within the Estabrook-Wahlquist prolongation scheme, without using explicit representations from the start. This procedure works generally forN-dimensional pseudopotentials.

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References

  1. H. D. Wahlquist andF. B. Estabrook:J. Math. Phys.,16, 1 (1975).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. J. Corones andF. J. Testa:Lecture Notes in Mathematics 515, edited byR. M. Miura (Springer, Berlin, 1976), p. 184.

    Google Scholar 

  3. M. Leo, R. A. LEO, L. Martina, F. A. E. Pirani andG. Soliani:Physica B,4, 105 (1981).

    MathSciNet  MATH  Google Scholar 

  4. M. Leo, R. A. Leo, G. Solani andL. Martina:Phys. Rev. D,26, 809 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  5. M. Leo, R. A. Leo, G. Soliani, L. Solombrino andL. Martina:J. Math. Phys.,24, 1720 (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Leo, R. A. Leo, L. Martina andG. Soliani:Prolongation theory of the three-wave resonant interaction, Preprint UL-DF-35-83/84:, University of Lecce, Italy (1984).

    Google Scholar 

  7. D. J. Kaup, A. H. Reiman andA. Bers:Rev. Mod. Phys.,51, 275 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  8. W. F. Shadwick:J. Math. Pays.,21, 454 (1980).

    MathSciNet  ADS  MATH  Google Scholar 

  9. H. D. Wahlquist andF. B. Estabrook:Phys. Rev. Lett.,31, 1386 (1973).

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica dell’ Università, Lecce, Italia

    M. Leo, R. A. Leo & G. Soliani

  2. Sezione di Bari, Istituto Nazionale di Fisica Nucleare, Italia

    M. Leo, R. A. Leo & G. Soliani

  3. Dipartimento di Fisica dell’Università, Lecce, Italia

    L. Martina

Authors
  1. M. Leo
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  2. R. A. Leo
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  3. G. Soliani
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  4. L. Martina
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Leo, M., Leo, R.A., Soliani, G. et al. On the use of closed non-Abelian prolongation algebras to find Bäcklund transformations of nonlinear evolution equations. Lett. Nuovo Cimento 41, 497–502 (1984). https://doi.org/10.1007/BF02748392

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  • DOI: https://doi.org/10.1007/BF02748392

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