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Approximation solutions of derivative nonlinear Schrödinger equation with computational applications by variational method

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Abstract

The derivative nonlinear Schrödinger (DNLS) equation is a nonlinear dispersive model that appears in the description of wave propagation in a plasma. The existence of a Lagrangian and the invariant variational principle for two coupled equations are given. The two coupled equations is describing the nonlinear evolution of the Alfvén wave with magnetosonic waves at much larger scale. A type of the coupled DNLS equations is studied by means of symbolic computation, which can describe the wave propagation in birefringent optical fibers. The functional integral corresponding to those equations is derived. We investigate the approximation solutions of the DNLS equation by choice of a trial function in the region of the rectangular box in two cases. By using this trial functions, the functional integral and the Lagrangian of the system without loss are found. The general case for the two-box potential can be obtained on the basis of a different ansatz, where we approximate the Jost function by series in the tanh function method instead of the piece-wise linear function.

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References

  1. W.-P. Zhonga, M. Beli, B.A. Malomedc, T. Huangb, Ann. Phys. 355, 313 (2015).

    Article  ADS  Google Scholar 

  2. E. Mjølhus, Phys. Scr. 40, 227 (1989).

    Article  ADS  Google Scholar 

  3. K. Ohkuma, Y.H. Ichikawa, Y. Abe, Opt. Lett. 12, 516 (1987).

    Article  ADS  Google Scholar 

  4. M. Daniel, V. Veerakumar, Phys. Lett. A 302, 77 (2002).

    Article  MathSciNet  ADS  Google Scholar 

  5. M. Li, J.-H. Xiao, W.-J. Liu, Y. Jiang, B. Tian, Commun. Nonlinear Sci. Numer. Simulat. 17, 2845 (2012).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. F. Wua, Z. Dai, Appl. Math. Comput. 218, 9305 (2012).

    Article  MathSciNet  Google Scholar 

  7. J.-L. Chena, C.-Q. Dai, X.-G. Wanga, Comput. Math. Appl. 62, 620 (2011).

    Article  MathSciNet  Google Scholar 

  8. S.A. Khuri, Appl. Math. Comput. 97, 251 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Biazar, B. Ghanbari, J. King Saud University Sci. 24, 33 (2012).

    Article  Google Scholar 

  10. A.K. Alomari, M.S.M. Noorani, R. Nazar, Commun. Nonlinear Sci. Numer. Simulat. 14, 2009 (1196).

    MathSciNet  Google Scholar 

  11. A. Mohebbi, M. Dehghan, J. Comput. Appl. Math. 225, 124 (2009).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  12. A.R. Seadawy, Appl. Math. Lett. 25, 687 (2012).

    Article  MATH  MathSciNet  Google Scholar 

  13. M.A. Helal, A.R. Seadawy, R.S. Ibrahim, Appl. Math. Comput. 219, 5635 (2013).

    Article  MATH  MathSciNet  Google Scholar 

  14. M.A. Helal, A.R. Seadawy, Phys. Scr. 80, 350 (2009).

    Article  Google Scholar 

  15. G.P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).

  16. S.K. Turitsyn, B.G. Bale, M.P. Fedoruk, Phys. Rep. 521, 135 (2012).

    Article  ADS  Google Scholar 

  17. F. Abdullaev, Theory of Solitons in Inhomogeneous Media (Wiley, New York, 1994).

  18. M.A. Helal, A.R. Seadawy, Z. Angew. Math. Phys. 62, 839 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  19. A.H. Khater, D.K. Callebaut, M.A. Helal, A.R. Seadawy, Eur. Phys. J. D 39, 237 (2006).

    Article  ADS  Google Scholar 

  20. A.H. Khater, M.A. Helal, A.R. Seadawy, Nuovo Cimento B 115, 1303 (2000).

    MathSciNet  ADS  Google Scholar 

  21. Y.Y. Wang, C.Q. Dai, X.G. Wang, Nonlinear Dyn. 77, 1323 (2014).

    Article  MathSciNet  Google Scholar 

  22. C.Q. Dai, X.G. Wang, G.Q. Zhou, Phys. Rev. A 89, 013834 (2014).

    Article  ADS  Google Scholar 

  23. H.P. Zhu, Nonlinear Dyn. 76, 1651 (2014).

    Article  Google Scholar 

  24. Y.X. Chen, Nonlinear Dyn. 79, 427 (2015).

    Article  Google Scholar 

  25. X. Lu, F. Lin, F. Qi, Appl. Math. Model. 39, 3221 (2015).

    Article  MathSciNet  Google Scholar 

  26. A.R. Seadawy, Comput. Math. Appl. 62, 3741 (2011).

    Article  MATH  MathSciNet  Google Scholar 

  27. A.R. Seadawy, K. El-Rashidy, Abstr. Appl. Anal. 2015, 369294 (2015).

    Article  MathSciNet  Google Scholar 

  28. A.R. Seadawy, Comput. Math. Appl. 70, 345 (2015).

    Article  MathSciNet  Google Scholar 

  29. K. Kondo, K. Kajiwara, K. Matsui, J. Phys. Soc. Jpn. 66, 60 (1997).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. E. Tonti, Acad. R. Belg. Bull. Cl. Sci. 55, 137 (1969).

    MATH  MathSciNet  Google Scholar 

  31. E. Tonti, Acad. R. Belg. Bull. Cl. Sci. 55, 262 (1969).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, Faculty of science, Taibah University, Al-Ula, Saudi Arabia

    Aly R. Seadawy

  2. Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Aly R. Seadawy

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  1. Aly R. Seadawy
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Correspondence to Aly R. Seadawy.

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Seadawy, A.R. Approximation solutions of derivative nonlinear Schrödinger equation with computational applications by variational method. Eur. Phys. J. Plus 130, 182 (2015). https://doi.org/10.1140/epjp/i2015-15182-5

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  • DOI: https://doi.org/10.1140/epjp/i2015-15182-5

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