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Highly dispersive optical solitons in the nonlinear Schrödinger’s equation having polynomial law of the refractive index change

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Abstract

In this paper, we apply the unified Riccati equation expansion method, as well as two forms of auxiliary equation methodology, to find highly dispersive optical solitons in the nonlinear Schrödinger’s equation having a polynomial law of the refractive index change. Bright, dark and singular solitons as well as periodic and Jacobi elliptic solutions are obtained that are presented together with their existence criteria.

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Acknowledgements

The research work of the sixth author (QZ) was supported by the National Natural Science Foundation of China (Grant Nos. 11705130 and 1157149); this author was also sponsored by the Chutian Scholar Program of Hubei Government in China. The research work of the ninth author (MRB) was supported by the Grant NPRP 11S-1246-170033 from QNRF, and he is thankful for it. The authors also declare that there is no conflict of interest. The authors wish to thank the referees for their constructive comments on the paper.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

    Elsayed M E Zayed, Mohamed E M Alngar & Mahmoud M El-Horbaty

  2. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL, 35762-7500, USA

    Anjan Biswas & Salam Khan

  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Anjan Biswas & Fouad Mallawi

  4. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria, 0008, South Africa

    Anjan Biswas

  5. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Shosse, Moscow, Russian Federation, 115409

    Anjan Biswas

  6. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100, Yozgat, Turkey

    Mehmet Ekici

  7. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China

    Qin Zhou

  8. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar

    Milivoj R Belic

Authors
  1. Elsayed M E Zayed
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  2. Mohamed E M Alngar
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  3. Mahmoud M El-Horbaty
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  4. Anjan Biswas
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  5. Mehmet Ekici
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  6. Qin Zhou
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  7. Salam Khan
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  8. Fouad Mallawi
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  9. Milivoj R Belic
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Corresponding author

Correspondence to Mohamed E M Alngar.

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Zayed, E.M.E., Alngar, M.E.M., El-Horbaty, M.M. et al. Highly dispersive optical solitons in the nonlinear Schrödinger’s equation having polynomial law of the refractive index change. Indian J Phys 95, 109–119 (2021). https://doi.org/10.1007/s12648-020-01694-7

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  • DOI: https://doi.org/10.1007/s12648-020-01694-7

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