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New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using Sardar sub-equation method

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Abstract

In this study, Sardar sub-equation method is employed to obtain the solitary wave solutions for generalized fractional Tzitzéica type equations. By utilizing this method, novel solutions are derived for Tzitzéica, Tzitzéica Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations in terms of fractional derivatives. The benefit of proposed method is that it offers a wide variety of soliton solutions, consisting of dark, bright, singular, periodic singular as well as combined dark-singular and combined dark–bright solitons. These solutions provide valuable insights into the intricate dynamics of generalized fractional Tzitzéica type evolution equations. The fractional wave and Painlevé transformation are utilized to transform the governing equation. The outcomes of our study are presented in a manner that highlights the practical utility and adeptness of fractional derivatives, along with the effectiveness of the proposed approach, in addressing a spectrum of nonlinear equations. Our findings reveal that the proposed method presents a comprehensive and efficient approach to explore exact solitary wave solutions for generalized fractional Tzitzeica type evolution equations.

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Acknowledgements

The authors express sincere gratitude to the University of Okara for their invaluable support. The authors are also thankful for the university’s continuous encouragement and the conducive research environment that facilitated the completion of this work.

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Authors and Affiliations

  1. Department of Biomedical Engineering, National Cheng Kung University, Tainan, 701401, Taiwan

    Dean Chou

  2. National Center for High-performance Computing, Hsinchu, 300092, Taiwan

    Dean Chou

  3. Department of Mathematics, University of Okara, Okara, Pakistan

    Hamood Ur Rehman & Aamna Amer

  4. Department of Physics, University of Sahiwal, Sahiwal, Pakistan

    Aatika Amer

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  1. Dean Chou
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  3. Aamna Amer
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Correspondence to Hamood Ur Rehman.

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Chou, D., Ur Rehman, H., Amer, A. et al. New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using Sardar sub-equation method. Opt Quant Electron 55, 1148 (2023). https://doi.org/10.1007/s11082-023-05425-0

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