A new representation for the nonlinear classical oscillator

Regular Article

Abstract

We use the q-exponential function defined by Tsallis to make a new representation of the classical nonlinear oscillator in which the solution of the correspondent differential equation is mapped in another nonlinear differential equation with the coordinate x(t) deformed in a new coordinate xq(t). The solution is given in the form of a sum of two complex q-exponential functions defined in the Tsallis theory. We obtain the correspondent nonlinear equation to this solution and derive some of its properties.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    C. Tsallis, J. Stat. Phys. 52, 479 (1988) ADSCrossRefGoogle Scholar
  2. 2.
    C. Tsallis, Introduction to nonextensive statistical mechanics (Springer, Santa Fé, New Mexico, 2009) Google Scholar
  3. 3.
    M. Jauregui, C. Tsallis, Phys. Lett. A 375, 2085 (2011) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    C. Tsallis, Int. J. Bifurc. Chaos 22, 1230030 (2012) CrossRefGoogle Scholar
  5. 5.
    M. Jauregui, C. Tsallis, J. Math. Phys. 51, 063304 (2010) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Eur. Phys. Lett. 97, 41001 (2012) ADSCrossRefGoogle Scholar
  7. 7.
    J. Havrda, F. Charvát, Kybernetika 3, 30 (1967) MathSciNetGoogle Scholar
  8. 8.
    Z. Daróczy, Inf. Comput. 16, 36 (1970) Google Scholar
  9. 9.
    L.J.L. Cirto, L.S. Lima, F.D. Nobre, J. Stat. Mech. 04, P04012 (2015) CrossRefGoogle Scholar
  10. 10.
    L.J.L. Cirto, V.R.V. Assis, C. Tsallis, Physica A 393, 286 (2014) ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    F.D. Nobre, C. Tsallis, Phys. Rev. E 68, 036115 (2003) ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    F.D. Nobre, M.A. Rego-Monteiro, C. Tsallis, Phys. Rev. Lett. 106, 140601 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    G. Habib, G. Kerschen, Physica D 332, 1 (2016) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    S. Fernandez-Garcia, M. Krupab, F. Clementa, Physica D 332, 9 (2016) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    S.H. Strogatz, Nonlinear dynamics and chaos (Addison-Wesley, Reading, MA, 1994) Google Scholar
  16. 16.
    T. Yamano, Physica A 305, 486 (2002) ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    E.P. Borges, J. Phys. A 31, 5281 (1998) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 76, 307 (2008) MathSciNetCrossRefGoogle Scholar
  19. 19.
    T. Oikonomou, G. Baris Gagci, Phys. Lett. A 374, 2225 (2010) ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    P. Guidottia, Y. Shaob, Nonlinear Anal. 150, 114 (2017) MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas GeraisBelo HorizonteBrazil

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