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Analytical and numerical solutions of the Schrödinger–KdV equation

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Abstract

The Schrödinger–KdV equation with power-law nonlinearity is studied in this paper. The solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The G′/G method is also used to integrate this equation. Subsequently, the variational iteration method and homotopy perturbation method are also applied to solve this equation. The numerical simulations are also given.

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References

  1. A-M Wazwaz, Appl. Math. Comput. 154, 713 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. D Kaya and S-M El Sayed, Phys. Lett. A313, 82 (2003)

    ADS  Google Scholar 

  3. S-A Zarea, Chaos, Solitons and Fractals 41, 979 (2009)

    Article  ADS  MATH  Google Scholar 

  4. J Liu, L Yangb and K Yang, Phys. Lett. A325, 268 (2004)

    ADS  Google Scholar 

  5. Y Wu, Differ. Integral Equ. 23, 569 (2010)

    MATH  Google Scholar 

  6. A Malik, F Chand and S C Mishra, Appl. Math. Comput. 216, 2596 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. G Ebadi and A Biswas, J. Franklin Inst. 347, 1391 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. G Ebadi and A Biswas, Commun. Nonlinear Sci. Numer. Simul. 16, 2377 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. G Ebadi and A Biswas, Math. Comput. Model. 53, 694 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. J-H He, Int. J. Non-Linear Mech. 34, 699 (1999)

    Article  ADS  MATH  Google Scholar 

  11. J-H He, Int. J. Mod. Phys. B20, 1141 (2006)

    ADS  Google Scholar 

  12. J-H He and X-H Wu, Chaos, Solitons and Fractals 29, 108 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. J-H He, G C Wu and F Austin, Nonlin. Sci. Lett. A1, 1 (2010)

    Google Scholar 

  14. A-M Wazwaz, Comput. Math. Appl. 54, 895 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. M Tatari and M Dehghan, Comput. Math. Appl. 58, 2160 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. B Batiha, M-S-M Noorani, I Hashim and K Batiha, Phys. Lett. A372, 822 (2008)

    MathSciNet  ADS  Google Scholar 

  17. L-M-B Assas, Chaos, Solitons and Fractals 38, 1225 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. N-H Sweilama and R-F Al-Barb, Comput. Math. Appl. 54, 993 (2007)

    Article  MathSciNet  Google Scholar 

  19. A-J-M Jawad, M-D Petković and A Biswas, Appl. Math. Comput. 217, 7039 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  20. M Labidi and K Omrani, Int. J. Numer. Methods Heat Fluid Flow 21(4), 377 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. J-H He, Comput. Methods Appl. Mech. Eng. 178, 257 (1999)

    Article  ADS  MATH  Google Scholar 

  22. J-H He, Appl. Math. Comput. 135, 73 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. J-H He, Chaos, Solitons and Fractals 26, 695 (2005)

    Article  ADS  MATH  Google Scholar 

  24. J-H He, Int. J. Mod. Phys. B20, 2561 (2006)

    ADS  Google Scholar 

  25. J-H He, Comput. Math. Appl. 57, 410 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. D D Ganji and M Refai, Phys. Lett. A356, 131 (2006)

    ADS  Google Scholar 

  27. H-L An and Y Chen, Appl. Math. Comput. 203, 125 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. J Biazar and H Aminikhahb, Comput. Math. Appl. 58, 2221 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. S Küçükarslan, Nonlinear Analysis: Real World Applications 10, 2264 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. A-K Alomari, M-S-M Noorani and R Nazar, J. Appl. Math. Comput. 31, 1 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. M-S-H Chowdhury, I Hashim and A-F Ismail, Proceedings of the World Congress on Engineering, London, UK, 2010, Vol. III

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Authors and Affiliations

  1. Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of Carthage, BP 743, La Marsa, 2070, Tunisia

    MANEL LABIDI

  2. Faculty of Mathematical Sciences, University of Tabriz, Tabriz, 51666-14766, Iran

    GHODRAT EBADI

  3. Department of Physics and Pre-Engineering, Delaware State University, Dover, DE 19901-2277, USA

    ESSAID ZERRAD

  4. Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA

    ANJAN BISWAS

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  1. MANEL LABIDI
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  2. GHODRAT EBADI
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  3. ESSAID ZERRAD
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  4. ANJAN BISWAS
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Correspondence to ANJAN BISWAS.

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LABIDI, M., EBADI, G., ZERRAD, E. et al. Analytical and numerical solutions of the Schrödinger–KdV equation. Pramana - J Phys 78, 59–90 (2012). https://doi.org/10.1007/s12043-011-0212-2

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  • DOI: https://doi.org/10.1007/s12043-011-0212-2

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