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Multiple types of exact solutions and conservation laws of new coupled \((2+1)\)-dimensional Zakharov–Kuznetsov system with time-dependent coefficients

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Abstract

This paper investigates the new coupled \((2+1)\)-dimensional Zakharov–Kuznetsov (ZK) system with time-dependent coefficients for multiple types of exact solutions by using the Lie symmetry transformation method. Similarity transformation reduces the system of equations into ordinary differential equations and further, these are solved for solutions having bright, dark and singular solitons as well as periodic waves. Also, the solutions appeared in terms of time-dependent coefficient \(\beta (t)\) and analysed graphically to show the effect of this arbitrary function. It is proved that the given system is nonlinear self-adjoint, and some conservation laws are obtained by applying the new conservation theorem.

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Acknowledgements

Bikramjeet Kaur wishes to thank the University Grants Commission (UGC), New Delhi, India for financial support under Grant No. (F1-17.1 / 2013-14 / MANF-2013-14-SIK-PUN-21763). Rajesh Kumar Gupta thanks the Council of Scientific and Industrial Research (CSIR), India for financial support under Grant No. 25(0257)\({/}\)16 / EMR-II.

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Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147 004, India

    Bikramjeet Kaur

  2. Department of Mathematics and Statistics, Central University of Punjab, Mansa Road, Bathinda, 151 001, India

    R K Gupta

  3. Department of Mathematics, School of Physical and Mathematical Sciences, Central University of Haryana, Mahendergarh, 123 031, India

    R K Gupta

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  1. Bikramjeet Kaur
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  2. R K Gupta
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Correspondence to R K Gupta.

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Kaur, B., Gupta, R.K. Multiple types of exact solutions and conservation laws of new coupled \((2+1)\)-dimensional Zakharov–Kuznetsov system with time-dependent coefficients. Pramana - J Phys 93, 59 (2019). https://doi.org/10.1007/s12043-019-1806-3

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  • DOI: https://doi.org/10.1007/s12043-019-1806-3

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