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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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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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Keywords

  • Lie’s infinitesimals criterion
  • exact solutions
  • new coupled \((2+1)\)-dimensional Zakharov–Kuznetsov system
  • conservation laws

PACS Nos

  • 02.20.Sv
  • 04.20.Jb
  • 02.30.Jr
  • 05.45.Yv