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A reduction technique to solve the (2+1)-dimensional KdV equations with time local fractional derivatives

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Abstract

This paper investigates the (2+1)-dimensional Korteweg-de Vries (KdV) equation with a local M-derivative and beta derivative in the time direction. Investigation on the (2+1)-dimensional Korteweg-de Vries (KdV) equation with a local M-derivative and beta derivative in the time direction is important because it provides insights into the behavior of nonlinear waves and has potential applications in various fields such as fluid dynamics, plasma physics, and optics. We apply Nucci’s reduction method to obtain exact solutions of this equation, including solitary wave solutions, periodic wave solutions, and rational solutions. Our results demonstrate the significant effects of the M-derivative and beta derivative on the solutions, including changes in the wave speed and the introduction of additional phase constants. Finally, we discuss the physical implications of these solutions. Overall, this work highlights the importance of considering local derivatives in the study of nonlinear partial differential equations and demonstrates the effectiveness of Nucci’s reduction method in obtaining exact solutions of the (2+1)-dimensional KdV equation.

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Authors and Affiliations

  1. Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey

    M. S. Hashemi

  2. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran

    M. Mirzazadeh

  3. Near East University, Operational Research Center in Healthcare, 99138, Nicosia, TRNC Mersin 10, Turkey

    Hijaz Ahmad

  4. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Hijaz Ahmad

  5. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186, Roma, Italy

    Hijaz Ahmad

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  1. M. S. Hashemi
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  2. M. Mirzazadeh
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  3. Hijaz Ahmad
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Contributions

Conceptualization: MM. Data curation: MM. Formal analysis: MSH, HA. Validation: MSH. Writing—original draft: MSH, MM. Writing—review editing: HA.

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Correspondence to Hijaz Ahmad.

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Hashemi, M.S., Mirzazadeh, M. & Ahmad, H. A reduction technique to solve the (2+1)-dimensional KdV equations with time local fractional derivatives. Opt Quant Electron 55, 721 (2023). https://doi.org/10.1007/s11082-023-04917-3

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