Solitons and conservation laws in magneto-optic waveguides with triple-power law nonlinearity
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RESEARCH ARTICLE
Solitons and conservation laws in magneto-optic waveguides with triple-power law nonlinearity Elsayed M. E. Zayed1 • Mohamed E. M. Alngar1 • Anjan Biswas2,3,4 • Abdul H. Kara5 • Luminita Moraru6 • Mehmet Ekici7 • Abdullah K. Alzahrani3 Milivoj R. Belic8
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Received: 2 August 2020 / Accepted: 25 August 2020 Ó The Optical Society of India 2020
Abstract The results of this paper stem from soliton solutions in magneto-optic waveguides that maintain triplepower law nonlinearity. Kudryashov’s method and generalized Jacobi’s elliptic function expansion collectively reveal a complete soliton solutions spectrum to the model. Finally, the conservation laws are also placed in the paper. Keywords Solitons Magneto-optics Triple-power law
& Mehmet Ekici [email protected] 1
Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2
Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-4900, USA
3
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4
Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Shosse, Moscow, Russian Federation 115409
5
School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South Africa
6
Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos University of Galati, 47 Domneasca Str., 800008 Galat¸ i, Romania
7
Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey
8
Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar
Introduction The study of optical solitons in a wide variety of waveguides has picked up momentum during the last couple of decades or so. These waveguides range from optical fibers, optical couplers, PCF, metamaterials, Bragg gratings, magneto-optic waveguides, plasmonics and various others [1–20]. Very recently, a plethora of results from magnetooptic waveguides, with various forms of refractive index, has been reported [1, 15–20]. Today’s results form a sequel to one such paper that is on magneto-optic waveguide which has been recently studied with polynomial law of nonlinear refractive index [18]. Such a law naturally generalizes to triple-power law of nonlinearity. Just like the prequel paper, the current work retrieves soliton solutions with the aid of Kudryashov’s algorithm as well as Jacobi’s elliptic function expansion. These two approaches collectively reveal bright, dark and singular optical solitons. The second scheme additionally reveals solutions to the model in terms of Weierstrass’ elliptic function that are also included, for a complete spectrum of solutions. Finally, the conservation laws are also located and listed. The details are enumerated in the rest of the paper after laying the mathematical foundations of the model. Governing model The coupled system of NLSE for magneto-optic waveguides having triple-power law nonlinearity is given by
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