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Exact solutions for fifth-order KdV-type equations with time-dependent coefficients using the Kudryashov method

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Abstract.

The KdV equation plays an important role in describing motions of long waves in shallow water under gravity, one-dimensional nonlinear lattice, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics and other areas. The KdV equation is a well-known model for the description of nonlinear long internal waves in a fluid stratified by both density and current. The aim of this paper is to present solitary wave solutions of the fifth-order KdV equations with time-dependent coefficients. The Kudryashov method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving high-order nonlinear partial differential equations with time-dependent coefficients in mathematical physics.

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References

  1. Anjan Biswas, Swapan Konar, Appl. Math. Lett. 20, 1122 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  2. Anjan Biswas, Essaid Zerrad, Swapan Konar, Commun. Nonlinear Sci. Numer. Simulat. 13, 1281 (2008)

    Article  ADS  MATH  Google Scholar 

  3. Anjan Biswas, Commun. Nonlinear Sci. Numer. Simulat. 14, 3503 (2009)

    Article  ADS  MATH  Google Scholar 

  4. Muhmmad S. Ismail, Anjan Biswas, Appl. Math. Comput. 216, 1673 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Houria Triki, Anjan Biswas, Waves Random Complex Media 21, 151 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. M. Mirzazadeh, M. Eslami, Eur. Phys. J. Plus 11, 1 (2013)

    Google Scholar 

  7. M. Eslami, M. Mirzazadeh, Rep. Math. Phys. 73, 77 (2014)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. M. Eslami, M. Mirzazadeh, Ocean Eng. 83, 133 (2014)

    Article  Google Scholar 

  9. N.A. Kudryashov, J. Appl. Math. Mech. 52, 361 (1988)

    Article  MathSciNet  Google Scholar 

  10. N.A. Kudryashov, Commun. Nonlinear Sci. Numer. Simulat. 17, 2248 (2012)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. N.A. Kudryashov, Phys. Lett. A 147, 287 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  12. N.A. Kudryashov, Phys. Lett. A 155, 269 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  13. M.M. Kabir, A. Khajeh, E. Abdi Aghdam, A. Yousefi Koma, Math. Methods Appl. Sci. 34, 213 (2011)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. P.N. Ryabov, Appl. Math. Comput. 217, 3585 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  15. H. Triki, A.-M. Wazwaz, Commun. Nonlinear Sci. Numer. Simulat. 19, 404 (2014)

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    M. Eslami

  2. Department of Engineering sciences, Faculty of Technology and Engineering East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran

    M. Mirzazadeh

Authors
  1. M. Eslami
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  2. M. Mirzazadeh
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Correspondence to M. Mirzazadeh.

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Eslami, M., Mirzazadeh, M. Exact solutions for fifth-order KdV-type equations with time-dependent coefficients using the Kudryashov method. Eur. Phys. J. Plus 129, 192 (2014). https://doi.org/10.1140/epjp/i2014-14192-1

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  • DOI: https://doi.org/10.1140/epjp/i2014-14192-1

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