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Conservation Laws for Solitons in Magneto-optic Waveguides with Anti-cubic and Generalized Anti-cubic Nonlinearities

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Abstract

This paper implements a multiplier approach to exhibit conservation laws in magneto-optic waveguides that maintain anti-cubic as well as generalized anti-cubic forms of the nonlinear refractive index. Three conservation laws are retrieved for each form of nonlinearity. They are power, linear momentum and Hamiltonian. The conserved quantities are computed from their respective densities.

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References

  1. Dötsch, H., Bahlmann, N., Zhuromskyy, O., Hammer, M., Wilkens, L., Gerhardt, R., Hertel, P., and Popkov, A. F., Applications of Magneto-Optical Waveguides in Integrated Optics: Review, J. Opt. Soc. Am. B, 2005, vol. 22, no. 1, pp. 240–253.

    Article  Google Scholar 

  2. Fedele, R., Schamel, H., Karpman, V. I., and Shukla, P. K., Envelope Solitons of Nonlinear Schrödinger Equation with an Anti-Cubic Nonlinearity, J. Phys. A, 2003, vol. 36, no. 4, pp. 1169–1173.

    Article  MathSciNet  Google Scholar 

  3. Haider, T., A Review of Magneto-Optic Effects and Its Application, Int. J. Electromagn. Appl., 2017, vol. 7, no. 1, pp. 17–24.

    Google Scholar 

  4. Hasegawa, K. and Miyazaki, Y., Magneto-Optic Devices Using Interaction between Magnetostatic Surface Wave and Optical Guided Wave, Jpn. J. Appl. Phys., 1992, vol. 31, pp. 230–233.

    Article  Google Scholar 

  5. Kudryashov, N. A., First Integrals and General Solution of the Traveling Wave Reduction for the Schrödinger Equation with Anti-Cubic Nonlinearity, Optik, 2019, vol. 185, pp. 665–671.

    Article  Google Scholar 

  6. Qiu, Y., Malomed, B. A., Mihalache, D., Zhu, X., Peng, J., and He, Y., Generation of Stable Multi-Vortex Clusters in a Dissipative Medium with Anti-Cubic Nonlinearity, Phys. Lett. A, 2019, vol. 383, no. 228, pp. 2579–2583.

    Article  MathSciNet  Google Scholar 

  7. Shoji, Y. and Mizumoto, T., Waveguide Magneto-Optical Devices for Photonics Integrated Circuits, Opt. Mater. Express, 2018, vol. 8, no. 8, pp. 2387–2394.

    Article  Google Scholar 

  8. Yan, Z., Chow, K. W., and Malomed, B. A., Exact Stationary Wave Patterns in Three Coupled Nonlinear Schrödinger/Gross – Pitaevskii Equations, Chaos Solitons Fractals, 2009, vol. 42, no. 5, pp. 3013–3019.

    Article  MathSciNet  Google Scholar 

  9. Zayed, E. M. E., Alngar, M. E. M., Shohib, R. M. A., Biswas, A., Ekici, M., Alzahrani, A. K., and Belic, M. R., Solitons in Magneto-Optic Waveguides with Anti-Cubic Nonlinearity, Optik, 2020, vol. 222, 165313, pp.

    Article  Google Scholar 

  10. Zayed, E. M. E., Alngar, M. E. M., El-Horbaty, M. M., Asma, M., Biswas, A., Ekici, M., Alzahrani, A. K., and Belic, M. R., Solitons in Magneto-Optic Waveguides with Generalized Anti-Cubic Nonlinearity, Optik, 2020, vol. 223, 165456, pp.

    Article  Google Scholar 

  11. Kudryashov, N. A., Safonova, D. V., and Biswas, A., Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan – Kundu – Lakshmanan Equation, Regul. Chaotic Dyn., 2019, vol. 24, no. 6, pp. 607–614.

    Article  MathSciNet  Google Scholar 

  12. Biswas, A., Kara, A. H., Zhou, Q., Alzahrani, A. K., and Belic, M. R., Conservation Laws for Highly Dispersive Optical Solitons in Birefringent Fibers, Regul. Chaotic Dyn., 2020, vol. 25, no. 2, pp. 166–177.

    Article  MathSciNet  Google Scholar 

  13. Gonzalez-Gaxiola, O., Biswas, A., Asma, M., and Alzahrani, A. K., Optical Dromions and Domain Walls with the Kundu – Mukherjee – Naskar Equation by the Laplace – Adomian Decomposition Scheme, Regul. Chaotic Dyn., 2020, vol. 25, no. 4, pp. 338–348.

    Article  MathSciNet  Google Scholar 

  14. Kudryashov, N. A., Highly Dispersive Optical Solitons of an Equation with Arbitrary Refractive Index, Regul. Chaotic Dyn., 2020, vol. 25, no. 6, pp. 537–543.

    Article  MathSciNet  Google Scholar 

  15. Kudryashov, N. A., Rational Solutions of Equations Associated with the Second Painlevé Equation, Regul. Chaotic Dyn., 2020, vol. 25, no. 3, pp. 273–280.

    Article  MathSciNet  Google Scholar 

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Funding

The research work of the sixth author (MRB) was supported by the grant NPRP 11S-1126-170033 from QNRF and he is thankful for it.

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Authors and Affiliations

  1. Department of Physics, Chemistry and Mathematics, Alabama A&M University, AL 35762–4900, Normal, USA

    Anjan Biswas

  2. Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Anjan Biswas & Abdullah K. Alzahrani

  3. Department of Applied Mathematics, National Research Nuclear University MEPhI, Kashirskoe sh. 31, 115409, Moscow, Russia

    Anjan Biswas

  4. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, Pretoria, South Africa

    Anjan Biswas

  5. School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits–2050, Johannesburg, South Africa

    Abdul H. Kara

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

    Mehmet Ekici

  7. Mathematics Department, Faculty of Science, Zagazig University, 44519, Zagazig, Egypt

    Elsayed M. E.

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

    Milivoj R. Belic

Authors
  1. Anjan Biswas
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  2. Abdul H. Kara
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  3. Mehmet Ekici
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  4. Elsayed M. E.
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  5. Abdullah K. Alzahrani
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  6. Milivoj R. Belic
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Corresponding authors

Correspondence to Anjan Biswas, Abdul H. Kara, Mehmet Ekici, Elsayed M. E., Abdullah K. Alzahrani or Milivoj R. Belic.

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The authors also declare that there is no conflict of interest.

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MSC2010

78A60

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Biswas, A., Kara, A.H., Ekici, M. et al. Conservation Laws for Solitons in Magneto-optic Waveguides with Anti-cubic and Generalized Anti-cubic Nonlinearities. Regul. Chaot. Dyn. 26, 456–461 (2021). https://doi.org/10.1134/S1560354721040080

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  • DOI: https://doi.org/10.1134/S1560354721040080

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