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Exact Traveling Wave Solutions and Bifurcation Analysis for Time Fractional Dual Power Zakharov-Kuznetsov-Burgers Equation

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Mathematical Modelling and Scientific Computing with Applications (ICMMSC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 308))

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Abstract

In this paper, we introduce the time fractional dual power Zakharov-Kuznetsov-Burgers equation in the sense of modified Riemann-Liouville derivative. We briefly describe one direct ansatz method namely \((G'/G)\)-expansion method in adherence of fractional complex transformation and applying this method exploit miscellaneous exact traveling wave solutions including solitary wave, kink-type wave, breaking wave and periodic wave solutions of the equation. Next we investigate the dynamical behavior, bifurcations and phase portrait analysis of the exact traveling wave solutions of the system in presence and absence of damping effect. Moreover, we demonstrate the exceptional features of the traveling wave solutions and phase portraits of planar dynamical system via interesting figures.

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Authors and Affiliations

  1. Department of Mathematics, Kazi Nazrul University, Asansol, 713340, India

    Amiya Das

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  1. Amiya Das
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Correspondence to Amiya Das .

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Editors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Santanu Manna

  2. Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL, USA

    Biswa Nath Datta

  3. Discipline of Mathematics, Indian Institute of Technology Indore, Indore, Madhya Pradesh, India

    Sk. Safique Ahmad

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Das, A. (2020). Exact Traveling Wave Solutions and Bifurcation Analysis for Time Fractional Dual Power Zakharov-Kuznetsov-Burgers Equation. In: Manna, S., Datta, B., Ahmad, S. (eds) Mathematical Modelling and Scientific Computing with Applications. ICMMSC 2018. Springer Proceedings in Mathematics & Statistics, vol 308. Springer, Singapore. https://doi.org/10.1007/978-981-15-1338-1_3

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