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Advanced exact solutions to the nano-ionic currents equation through MTs and the soliton equation containing the RLC transmission line

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Abstract

In this study, the double (G′/G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G′/G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions.

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Acknowledgements

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: (23UQU4410172DSR002).

Author information

Authors and Affiliations

  1. Department of Mathematics, Bangladesh Army University of Engineering & Technology, Natore, 6431, Bangladesh

    M. Akher Chowdhury

  2. Department of Mathematics, Khulna University of Engineering & Technology, Khulna, 9203, Bangladesh

    M. Mamun Miah

  3. Division of Mathematical and Physical Sciences, Kanazawa University, Kakuma, Kanazawa, 920-1192, Japan

    M. Mamun Miah

  4. Department of Mathematics and Physics, Khulna Agricultural University, Khulna, 9100, Bangladesh

    M. Ashik Iqbal

  5. Mathematics Department, Faculty of Science, King Abdulaziz University, Jeddah, 21521, Saudi Arabia

    Hashim M. Alshehri

  6. Department of Mathematics, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  7. Institute of Space Sciences, 077125, Magurele, Bucharest, Romania

    Dumitru Baleanu

  8. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Dumitru Baleanu

  9. Department of Mathematics, Faculty of Applied Science, Umm Al-Qura University, Makkah, 21955, Saudi Arabia

    M. S. Osman

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  1. M. Akher Chowdhury
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  2. M. Mamun Miah
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  3. M. Ashik Iqbal
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  4. Hashim M. Alshehri
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  5. Dumitru Baleanu
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  6. M. S. Osman
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Correspondence to Dumitru Baleanu or M. S. Osman.

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Chowdhury, M.A., Miah, M.M., Iqbal, M.A. et al. Advanced exact solutions to the nano-ionic currents equation through MTs and the soliton equation containing the RLC transmission line. Eur. Phys. J. Plus 138, 502 (2023). https://doi.org/10.1140/epjp/s13360-023-04105-y

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