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Exact solutions, conservation laws, bifurcation of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver equation

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Abstract

In the present work, we observe the dynamical behavior of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver (STO) equation. Exact solutions are derived using \({1}/{G^{^{\prime }}}\) expansion and modified Kudryashov methods. The wave transformation is used to transform STO equation into an ordinary differential equation. Combining Runge–Kutta fourth-order and Fourier spectral technique, we use a mixed scheme for the numerical study of STO equation. Since spectral methods expand the solution in trigonometric series resulting into higher-order technique and Runge–Kutta produces improved accuracy, we extract these qualities for a mixed scheme. Results so produced are presented graphically which provide a useful information about the dynamical behavior. Bifurcation behavior of nonlinear and supernonlinear traveling waves of STO equation is studied with the help of bifurcation theory of planar dynamical systems. It is observed that STO equation supports nonlinear solitary wave, periodic wave, shock wave, stable oscillatory wave and most important supernonlinear periodic wave.

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Authors and Affiliations

  1. Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Fast, Lahore Campus, Lahore, Pakistan

    Muhammad Nasir Ali & Syed Muhammad Husnine

  2. Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Majitar, Rangpo, East-Sikkim, 737136, India

    Asit Saha

  3. Department of Mathematics, University of Dhaka, Dhaka, 1000, Bangladesh

    Samir Kumar Bhowmik

  4. Department of Mathematics, Central University of Haryana, Haryana, 123029, India

    Sharanjeet Dhawan

  5. Armutlu Vocational School, Yalova University, 77500, Armutlu, Yalova, Turkey

    Turgut Ak

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  1. Muhammad Nasir Ali
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  4. Samir Kumar Bhowmik
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Correspondence to Turgut Ak.

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Ali, M.N., Husnine, S.M., Saha, A. et al. Exact solutions, conservation laws, bifurcation of nonlinear and supernonlinear traveling waves for Sharma–Tasso–Olver equation. Nonlinear Dyn 94, 1791–1801 (2018). https://doi.org/10.1007/s11071-018-4457-x

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  • DOI: https://doi.org/10.1007/s11071-018-4457-x

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