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Nonlinear time fractional Korteweg-de Vries equations for the interaction of wave phenomena in fluid-filled elastic tubes

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Abstract.

This work investigates the wave-wave interactions by considering two-sided time fractional Korteweg-de Vries equations (TFKdVEs). The generalized \(\exp(-\Phi(\xi))\)-expansion method (GEEM) along with Khalil's fractional derivatives is employed to divulge several types of scattered wave solutions of TFKdVEs. It is found that the fractional parameters significantly modified the interaction of nonlinear wave dynamics. The results obtained may be useful for clarifications of the interaction between two waves not only in non-conservative fluid-filled elastic tubes but also in shallow water and plasma physics.

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Authors and Affiliations

  1. Department of Mathematics, Chittagong University of Engineering and Technology, 4349, Chittagong, Bangladesh

    F. Ferdous & M. G. Hafez

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  1. F. Ferdous
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  2. M. G. Hafez
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Correspondence to M. G. Hafez.

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Ferdous, F., Hafez, M.G. Nonlinear time fractional Korteweg-de Vries equations for the interaction of wave phenomena in fluid-filled elastic tubes. Eur. Phys. J. Plus 133, 384 (2018). https://doi.org/10.1140/epjp/i2018-12195-6

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  • DOI: https://doi.org/10.1140/epjp/i2018-12195-6

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