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On group-invariant solutions of Konopelchenko–Dubrovsky equation by using Lie symmetry approach

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Abstract

In the present study, we have applied similarity transformation method via Lie symmetry approach on the Konopelchenko–Dubrovsky (KD) equation. We have generated infinite-dimensional Lie algebra and commutation relations of the KD equation. The KD equation reduced into a system of ordinary differential equations (ODEs) by employing similarity reductions. Ultimately, the exact solutions of such system of ODEs provided various families of new group-invariant solutions of the KD equation. Furthermore, we have discussed the dynamics of each solution such as multisoliton, doubly solitons, periodic multisoliton, multiple wavefront, solitons interactions, parabolic and stationary wave through their evolution profiles. Numerical simulations have been performed by taking appropriate choices of arbitrary functions and constants involved in the solutions.

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Acknowledgements

One of the authors, Atul Kumar Tiwari, is grateful to CSIR-UGC, New Delhi, for the award of Senior Research Fellowship to writing this manuscript.

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  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad, 211004, India

    Mukesh Kumar & Atul Kumar Tiwari

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  1. Mukesh Kumar
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  2. Atul Kumar Tiwari
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Correspondence to Mukesh Kumar.

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Kumar, M., Tiwari, A.K. On group-invariant solutions of Konopelchenko–Dubrovsky equation by using Lie symmetry approach. Nonlinear Dyn 94, 475–487 (2018). https://doi.org/10.1007/s11071-018-4372-1

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  • DOI: https://doi.org/10.1007/s11071-018-4372-1

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