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Dynamical behaviour of nondissipative double dispersive microstrain wave in the microstructured solids

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Abstract

This work is interested in studying nondissipative double dispersive microstrain wave in the microstructured solids. Using a certain transformation, the basic equation is transformed into an ordinary differential equation that turns into a two-dimensional dynamical system corresponding to a one-dimensional Hamiltonian. Based on qualitative theory of dynamical systems, we consider some qualitative analyses of this system and use a conserved quantity to construct some traveling wave solutions. These solutions are illustrated graphically. We study the degeneracy of these solutions through the transmission between the orbits for different values of the included parameters. Moreover, we numerically study the quasiperiodic solution for the perturbed system after adding certain periodic forces to the main equation.

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Acknowledgements

The authors acknowledge the Deanship of Scientific Research at king Faisal University for the financial support under Nasher Track (Grant No. 216020)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa, 31982, Saudi Arabia

    M. E. Elbrolosy & A. A. Elmandouh

  2. Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt

    M. E. Elbrolosy

  3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

    A. A. Elmandouh

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  1. M. E. Elbrolosy
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Correspondence to M. E. Elbrolosy.

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Elbrolosy, M.E., Elmandouh, A.A. Dynamical behaviour of nondissipative double dispersive microstrain wave in the microstructured solids. Eur. Phys. J. Plus 136, 955 (2021). https://doi.org/10.1140/epjp/s13360-021-01957-0

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