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New Approach to Identifying Solitary Wave Solutions of Modified Kawahara Equation

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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Abstract

Stationary localized waves are considered in the frame moving to the right. The original ill–posed problem has a non–unique solution. To cope with this issue, the bifurcation problem is reformulated into a problem for identification of an unknown coefficient from over-posed boundary data in which the trivial solution is excluded. This approach to solving the modified fifth order Kawahara equation is original allowing identification of the non–trivial solutions. The numerical solutions are compared with known analytical solution. The convergence of the difference scheme is illustrated with numerical examples.

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References

  1. Araruna, F., Capistrano-Filho, R., Doronin, G.: Energy decay for the modified Kawahara equation posed in a bounded domain. J. Math. Anal. Appl. 385, 743–756 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bekir, A., Güner, Ö., Bilgil, H.: Optical soliton solutions for the variable coefficient modified Kawahara equation. Optik 126, 2518–2522 (2015)

    Article  Google Scholar 

  3. Biswas, A.: Solitary wave solution for the generalized Kawahara equation. Appl. Math. Lett. 22, 208–210 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Christov, C.I.: A method for identifying homoclinic trajectories. In: Proceedings of the 14th Spring Conference, Union of Bulgarian Mathematicians, pp. 571–577 (1985)

    Google Scholar 

  5. Hadamard, J.: Le Probleme de Cauchy et les Equations aux Derivatives Partielles Lineares Hyperboliques. Hermann, Paris (1932)

    MATH  Google Scholar 

  6. He, J.H.: Variational iteration method for delay differential equations. Commun. Nonlinear Sci. Numer. Simul. 2(4), 235–236 (1997)

    Article  Google Scholar 

  7. Jabbari, A., Kheiri, H.: New exact traveling wave solutions for the Kawahara and Modified Kawahara Equations by using Modified Tanh-Coth Method. Acta Universitatis Apulensis 23, 21–38 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Jin, L.: Application of variational iteration method and homotopy perturbation method to the modified Kawahara equation. Math. Comput. Model. 49, 573–578 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kawahara, T.: Oscillatory solitary waves in dispersive media. J. Phys. Soc. Jpn. 33, 260–264 (1972)

    Article  Google Scholar 

  10. Marinov, T.T., Christov, C.I., Marinova, R.S.: Novel numerical approach to solitary-wave solutions identification of Boussinesq and Korteweg-de Vries equations. Int. J. Bifurcat. Chaos 15(2), 557–565 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yusufoğlu, E., Bekir, A.: Symbolic computation and new families of exact travelling solutions for the Kawahara and modified Kawahara equations. Comput. Math. Appl. 55, 1113–1121 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zarebnia, M., Aghili, M.: A new approach for numerical solution of the modified Kawahara equation. J. Nonlinear Anal. Appl. 2, 48–59 (2016)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Natural Sciences, Southern University at New Orleans, 6801 Press Drive, New Orleans, LA, 70126, USA

    Tchavdar T. Marinov

  2. Department of Mathematical and Physical Sciences, Concordia University of Edmonton, 7128 Ada Boulevard, Edmonton, AB, T5B 4E4, Canada

    Rossitza S. Marinova

Authors
  1. Tchavdar T. Marinov
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  2. Rossitza S. Marinova
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Corresponding author

Correspondence to Rossitza S. Marinova .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Marinov, T.T., Marinova, R.S. (2018). New Approach to Identifying Solitary Wave Solutions of Modified Kawahara Equation. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_58

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_58

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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