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1-Soliton and peaked solitary wave solutions of nonlinear longitudinal wave equation in magneto–electro–elastic circular rod

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Abstract

In this paper, 1-soliton and two kinds of peaked solitary wave solutions of nonlinear longitudinal wave equation in magneto–electro–elastic circular rod are presented for the first time. The soliton ansatz will be applied to give 1-soliton solution; then, peaked solitary wave solutions are obtained by using direct integration with boundary condition and symmetry condition. At last, numeric graphs are provided for solitary wave solutions.

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References

  1. Xue, C.X., Pan, E., Zhang, S.Y.: Solitary waves in a magneto–electro–elastic circular rod. Smart Mater. Struct. 20, 105010 (2011)

    Article  Google Scholar 

  2. Khan, Kamruzzaman, et al.: Exact traveling wave solutions of an autonomous system via the enhanced \((\frac{G^{\prime }}{G})\)-expansion method. Waves Random Complex Media 25, 644–655 (2015)

    Article  MathSciNet  Google Scholar 

  3. Younis, Muhammad, Ali, Safdar: Bright, dark, and singular solitons in magneto–electro–elastic circular rod. Waves Random Complex Media 25, 549–555 (2015)

    Article  MathSciNet  Google Scholar 

  4. Zhou, Qin: Analytical study of solitons in magneto–electro–elastic circular rod. Nonlinear Dyn. 83, 1403–1408 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Liu, Z., Zhang, S.: Nonlinear waves and periodic solution in finite deformation elastic rod. Acta Mech. Solida Sin. 19, 1 (2006)

    Article  Google Scholar 

  6. Biswas, Anjan, Kara, A.H.: 1-Soliton solution and conservation laws for nonlinear wave equation in semiconductors. Appl. Math. Comput. 217, 4289–4292 (2010)

  7. Biswas, A.: 1-soliton solution of the generalized Zakharov–Kuznetsovmodified equalwidth equation. Appl. Math. Lett. 22, 1775 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Biswas, A., Zerrad, E.: Solitary wave solution of the Zakharov–Kuznetsov equation in plasmas with power law nonlinearity. Nonlinear Anal. Real World Appl. 11, 3272 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Suarez, P., Biswas, A.: Exact 1-soliton solution of the Zakharov equation in plasmas withpower law nonlinearity. Appl. Math. Comput. 217, 7372 (2011)

    MathSciNet  MATH  Google Scholar 

  10. Shijun, Liao: Two kinds of peaked solitary waves of the KdV, BBM and Boussinesq equations. Sci. China Phys. Mech. Astron. 55, 2469–2475 (2012)

    Google Scholar 

  11. Biswas, A., Mirzazadeh, M., Eslami, M.: Soliton solution of generalized chiral nonlinear schrodinger’s equation with time-dependent coefficients. Acta Phys. Pol. B 45, 849–866 (2014)

    Article  MathSciNet  Google Scholar 

  12. Krishnan, E.V., Ghabshi, M.A., Mirzazadeh, M., Bhrawy, A.H., Biswas, A., Belic, M.: Optical solitons for quadratic law nonlinearity with five integration schemes. J. Comput. Theor. Nanosci. 12, 4809–4821 (2015)

    Google Scholar 

  13. Zhou, Q., Mirzazadeh, M.: Analytical solitons for Langmuir waves in plasma physics with cubic nonlinearity and perturbations. Z. Naturforsch. A 71, 807–815 (2016)

    Google Scholar 

  14. Mirzazadeh, M.: Analytical study of solitons to nonlinear time fractional parabolic equations. Nonlinear Dyn. 85, 2569–2576 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Shaojie Yang & Tianzhou Xu

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  1. Shaojie Yang
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  2. Tianzhou Xu
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Correspondence to Shaojie Yang.

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Yang, S., Xu, T. 1-Soliton and peaked solitary wave solutions of nonlinear longitudinal wave equation in magneto–electro–elastic circular rod. Nonlinear Dyn 87, 2735–2739 (2017). https://doi.org/10.1007/s11071-016-3223-1

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  • DOI: https://doi.org/10.1007/s11071-016-3223-1

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