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New soliton solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity

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Abstract

In this paper, we consider a new class of conformable fractional derivative for constructing new exact solitary wave solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity, which describes the effects of quantic nonlinearity on the ultrashort optical solitons pulse propagation in non-Kerr media.These solitary wave solutions demonstrate the fact that solutions to the perturbed nonlinear Schrodinger equation with power law nonlinearity model can exhibit a variety of behaviors. For more illustration we consider the graphs for one of the solutions. It show that with changing \(\alpha \) (if \(\alpha \) tends to one; \(\alpha \) is fractional symbol) the graphs of the solutions of fractional perturbed nonlinear Schrodinger equation with power law nonlinearity is near to graph of solution of perturbed nonlinear Schrodinger equation with power law nonlinearity in general form.

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References

  1. Abdeljawad, T., Horani, M.A.L., Khalil, R.: Conformable fractional semigroup operators. J. Semigroup Theory Appl. 2015, Article ID. 7 (2015)

  2. Abdeljawad, Thabet: On conformable fractional calculus. J. Comput. Appl. Math. 279(1), 57–66 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Abu Hammad, M., Khalil, R.: Conformable heat differential equation. Int. J. Pure Appl. Math. 94(2), 215–221 (2014)

    Article  MATH  Google Scholar 

  4. Ei-Wakil, S.A.: New exact travelling wave solutions using modified extended tanh-function method. Chaos Solitons Fractals 31, 840–852 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Jumarie, G.: Modified Riemann–Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51, 1367–1376 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kilbas, A.A., Srivastava, M.H., Trujillo, J.J.: Theory and Application of Fractional Differential Equations. In: North Holland Mathematics Studies, vol. 204 (2006)

  8. Kilbas, A.A., Saigo, M.: On solution of integral equation of Abel–Volterra type. Differ. Integral Equ. 8(5), 993–1011 (1995)

    MathSciNet  MATH  Google Scholar 

  9. Liu, C.-S.: Counterexamples on Jumarie’s two basic fractional calculus formulae. Commun. Nonlinear Sci. Numer. Simul. (2014). doi:10.1016/j.cnsns.2014.07.022

  10. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

  11. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  12. Samko, S., Kilbas, A.A.: Marichev, Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Yverdon (1993)

    MATH  Google Scholar 

  13. Sarma, A.K., Saha, M., Biswas, A.: Optical solitons with power law nonlinearity and Hamiltonian perturbations: an exact solution. J. Infrared Milli. Terahertz Waves 31(9), 1048–1056 (2010)

    Article  Google Scholar 

  14. Shang, Y.D., Huang, H., Yuan, W.J.: The extended hyperbolic functions method and new exact solutions to the Zakharov equations. Appl. Math. Comput. 200, 110–122 (2008)

    MathSciNet  MATH  Google Scholar 

  15. Wang, M.L., Zhou, Y.B., Li, Z.B.: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys. Lett. A 216, 67–75 (1996)

    Article  MATH  Google Scholar 

  16. Wang, Q.: A new Riccati equation rational expansion method and its application to \((2 + 1)\)-dimensional Burgers equation. Chaos Solitons Fractals 25, 1019–1028 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yan, Z.Y.: New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water. Phys. Lett. A 285, 355–362 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yan, C.: A simple transformation for nonlinear waves. Phys. Lett. A 224, 77–84 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang, Z.Y.: New exact traveling wave solutions for the nonlinear Klein–Gordon equation. Turk. J. Phys. 32, 235–240 (2008)

    Google Scholar 

  20. Zhang, Z.Y., Liu, Z.H., Miao, X.J., Chen, Y.Z.: New exact solutions to the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity. Appl. Math. Comput. 216, 3064–3072 (2010)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

The author would like to express thanks to the editor and anonymous referees for their useful and valuable comments and suggestions.

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  1. Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran

    A. Neirameh

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  1. A. Neirameh
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Neirameh, A. New soliton solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity. SeMA 73, 309–323 (2016). https://doi.org/10.1007/s40324-016-0070-4

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  • DOI: https://doi.org/10.1007/s40324-016-0070-4

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