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Exact solutions to a class of nonlinear Schrödinger-type equations

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Abstract

A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).

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References

  1. A A Rangwala and J A Rao, J. Math. Phys. 31, 1126 (1990)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. W G Zhang, Comm. Appl. Math. Comput. 8(2), 45 (1994) (in Chinese)

    Google Scholar 

  3. V S Gerdjikov and I Ivanov, Bulg. J. Phys. 10, 130 (1983)

    Google Scholar 

  4. H H Chen, Y C Lee and C S Liu, Phys. SCR., 20, 490 (1979)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. M J Ablowitz, A Ramani and H A Segur, J. Math. Phys. 21, 1006 (1980)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. M J Ablowitz and P A Clarkson, Solitons, nonlinear evolution equations and inverse scattering transform (Cambridge University Press, Cambridge, 1991)

    Google Scholar 

  7. R Hirota, J. Math. Phys. 14, 810 (1973)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. S K Liu, T Fu, S D Liu and Q Zhao, Phys. Lett. A289, 69 (2001)

    ADS  MathSciNet  Google Scholar 

  9. Z Y Yan, Chaos, Solitons & Fractals 18, 299 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. R Conte and M Musette, J. Phys. A: Math. Gen. 25, 5609 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. E J Parkes and B R Duffy, Comput. Phys. Commun. 98, 288 (1996)

    Article  MATH  ADS  Google Scholar 

  12. Z B Li and Y P Liu, Comput. Phys. Commun. 148, 256 (2002)

    Article  ADS  Google Scholar 

  13. E G Fan, Phys. Lett. A277, 212 (2000)

    ADS  Google Scholar 

  14. E Yomba, Chaos, Solitons & Fractals 20, 1135 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. M L Wang and X Z Li, Phys. Lett. A343, 48 (2005)

    ADS  Google Scholar 

  16. M L Wang and X Z Li, Chaos, Solitons & Fractals 27, 477 (2006)

    Article  MathSciNet  Google Scholar 

  17. Y J Ren and H Q Zhang, Chaos, Solitons & Fractals 27, 959 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  18. J L Zhang, M L Wang, D M Cheng, et al, Commun. Theor. Phys. 40, 129 (2003)

    MathSciNet  Google Scholar 

  19. J L Zhang, D F Ren, M L Wang et al, Chin. Phys. 12, 825 (2003)

    Article  ADS  Google Scholar 

  20. Y M Wang, X Z Li, S Yang and M L Wang, Commun. Theor. Phys. 44, 396 (2005)

    Article  MathSciNet  Google Scholar 

  21. J L Zhang, D F Ren, M L Wang, et al, Acta Math. Sientia A25(2), 213 (2005)

    MathSciNet  Google Scholar 

  22. M L Wang, Phys. Lett. A199, 169 (1995)

    ADS  Google Scholar 

  23. M L Wang, Phys. Lett. A213, 279 (1996)

    ADS  Google Scholar 

  24. J F Zhang, Chin. Phys. 11, 425 (2002)

    Article  ADS  Google Scholar 

  25. E G Fan and H Q Zhang, Acta Phys. Sin. 47, 353 (1998)

    MathSciNet  Google Scholar 

  26. G N Xia et al, Appl. Math. Mech. 23, 52 (2002)

    Google Scholar 

  27. M L Wang and Y M Wang, Phys. Lett. A287, 211 (2001)

    ADS  Google Scholar 

  28. E G Fan and H Q Zhang, Acta Phys. Sin. 49, 1409 (2000)

    Google Scholar 

  29. J L Zhang, Y M Wang, M L Wang, et al, Chin. Phys. 12, 245 (2003)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. College of Science, Henan University of Science and Technology, 471003, Luoyang, China

    Jin-Liang Zhang & Ming-Liang Wang

  2. Department of Mathematics, Lanzhou University, 730000, Lanzhou, China

    Ming-Liang Wang

Authors
  1. Jin-Liang Zhang
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  2. Ming-Liang Wang
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Zhang, JL., Wang, ML. Exact solutions to a class of nonlinear Schrödinger-type equations. Pramana - J Phys 67, 1011–1022 (2006). https://doi.org/10.1007/s12043-006-0019-8

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  • DOI: https://doi.org/10.1007/s12043-006-0019-8

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