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Construction of Functional Closed Form Wave Solutions to the ZKBBM Equation and the Schrödinger Equation

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Abstract

The time fractional (1+1)-dimensional Schrödinger equation and the space–time fractional (1+1)-dimensional Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation are important mathematical models to interpret signal processing in optical fibers, the fractional quantum mechanics, water waves due to gravity, the motion of turbulent flows, the wave of driving flow of fluid, the ion osculate waves in plasma, etc. In the present article, we have examined the closed form soliton solutions with the assistance of the modified simple equation method together with the fractional wave transformation. The form of the attained solutions is rational, trigonometry and hyperbolic functions. We have shown that the assigned method is further general, efficient, straightforward and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering. We have depicted the figures of the evaluated solutions in order to interpret the physical phenomena.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Erciyes University, 38039, Melikgazi, Kayeri, Turkey

    Onur Alp Ilhan

  2. Department of Mathematics, Islamic University-Kushtia, Kushtia, Bangladesh

    M. Nurul Islam

  3. Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh

    M. Ali Akbar

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  1. Onur Alp Ilhan
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  2. M. Nurul Islam
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  3. M. Ali Akbar
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Correspondence to Onur Alp Ilhan.

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Ilhan, O.A., Islam, M.N. & Akbar, M.A. Construction of Functional Closed Form Wave Solutions to the ZKBBM Equation and the Schrödinger Equation. Iran J Sci Technol Trans Mech Eng 45, 827–840 (2021). https://doi.org/10.1007/s40997-020-00358-5

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