Optical solitons of the complex Ginzburg-Landau equation having dual power nonlinear form using $\varphi^{6}$-model expansion approach

Year 2023, Volume: 3 Issue: 3, 188 - 215, 30.09.2023

Muhammad Abubakar Isah , Asıf Yokuş

https://doi.org/10.53391/mmnsa.1337648

Cited By: 1

Abstract

This paper employs a novel $\varphi ^{6}$-model expansion approach to get dark, bright, periodic, dark-bright, and singular soliton solutions to the complex Ginzburg-Landau equation with dual power-law non-linearity. The dual-power law found in photovoltaic materials is used to explain nonlinearity in the refractive index. The results of this paper may assist in comprehending some of the physical effects of various nonlinear physics models. For example, the hyperbolic sine arises in the calculation of the Roche limit and the gravitational potential of a cylinder, the hyperbolic tangent arises in the calculation of the magnetic moment and the rapidity of special relativity, and the hyperbolic cotangent arises in the Langevin function for magnetic polarization. Frequency values, one of the soliton's internal dynamics, are used to examine the behavior of the traveling wave. Finally, some of the obtained solitons' three-, two-dimensional, and contour graphs are plotted.

Keywords

$\varphi ^{6}$-model expansion method, complex Ginzburg-Landau equation, soliton solutions, dual power-law nonlinearity

References

• Isah, M.A. and Külahçı, M.A. A study on null cartan curve in Minkowski 3-space. Applied Mathematics and Nonlinear Sciences, 5(1), 413-424, (2020).
• Isah, M.A. and Külahçı, M.A. Special curves according to bishop frame in Minkowski 3-space. Applied Mathematics and Nonlinear Sciences, 5(1), 237-248, (2020).
• Isah, M.A., Isah, I., Hassan, T.L. and Usman, M. Some characterization of osculating curves according to darboux frame in three dimensional euclidean space. International Journal of Advanced Academic Research, 7(12), 47-56, (2021).
• Isah, I., Isah, M.A., Baba, M.U., Hassan, T.L. and Kabir, K.D. On integrability of silver Riemannian structure. International Journal of Advanced Academic Research, 7(12), 2488-9849, (2021).
• Myint-U, T. and Lokenath, D. Linear Partial Differential Equations for Scientists and Engineers. Springer Science & Business Media: Berlin/Heidelberg, Germany, (2007).
• Ueda, T. and Kath, W.L. Dynamics of coupled solitons in nonlinear optical fibers. Physical Review A, 42(1), 563, (1990).
• Hasegawa, A. and Matsumoto, M. Optical solitons in fibers. In Springer Series in Photonics (Vol 9) (pp. 41-59). Berlin, Heidelberg: Springer, (1989).
• Musslimani, Z.H., Makris, K.G., El-Ganainy, R. and Christodoulides, D.N. Optical solitons in P T periodic potentials. Physical Review Letters, 100(3), 030402, (2008).
• Kivshar, Y.S. and Agrawal, G.P. Optical Solitons: from Fibers to Photonic Crystals. Academic Press, (2003).
• Hasegawa, A. and Kodama, Y. Signal transmission by optical solitons in monomode fiber. Proceedings of the IEEE, 69(9), 1145-1150, (1981).
• Manafian, J. and Heidari, S. Periodic and singular kink solutions of the Hamiltonian amplitude equation. Advanced Mathematical Models & Applications, 4(2), 134-149, (2019).
• Yokus, A. and Isah, M.A. Investigation of internal dynamics of soliton with the help of traveling wave soliton solution of Hamilton amplitude equation. Optical and Quantum Electronics, 54, 528, (2022).
• Yokus, A. and Isah, M.A. Stability analysis and solutions of (2 + 1)-Kadomtsev–Petviashvili equation by homoclinic technique based on Hirota bilinear form. Nonlinear Dynamics, 109, 3029-3040, (2022).
• Duran, S., Yokuş, A., Durur, H. and Kaya, D. Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics. Modern Physics Letters B, 35(26), 2150363, (2021).
• Joshi, H., Yavuz, M. and Stamova, I. Analysis of the disturbance effect in intracellular calcium dynamic on fibroblast cells with an exponential kernel law. Bulletin of Biomathematics, 1(1), 24-39, (2023).
• Yel, G., Kayhan, M. and Ciancio, A. A new analytical approach to the (1+ 1)-dimensional conformable Fisher equation. Mathematical Modelling and Numerical Simulation with Applications, 2(4), 211-220, (2022).
• Iskenderoglu, G. and Kaya, D. Chirped self-similar pulses and envelope solutions for a nonlinear Schrödinger’s in optical fibers using Lie group method. Chaos, Solitons & Fractals, 162, 112453, (2022).
• Ghanbari, B. and Baleanu, D. A novel technique to construct exact solutions for nonlinear partial differential equations. The European Physical Journal Plus, 134(10), 506, (2019).
• Kaya, D., Yokus, A. and Demiro˘glu, U. Comparison of exact and numerical solutions for the Sharma–Tasso–Olver equation. In Numerical Solutions of Realistic Nonlinear Phenomena (Vol 31) (pp. 53-65). Cham: Springer, (2020).
• Duran, S., Durur, H., Yavuz, M. and Yokus, A. Discussion of numerical and analytical techniques for the emerging fractional order Murnaghan model in materials science. Optical and Quantum Electronics, 55(6), 571, (2023).
• Durur, H., Yokus, A. and Yavuz, M. (2022). Behavior analysis and asymptotic stability of the traveling wave solution of the Kaup-Kupershmidt equation for conformable derivative. In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena, (Vol 3) (pp. 162-185). Bentham Science.
• Shafqat, R., Niazi, A.U.K., Yavuz, M., Jeelani, M. . and Saleem, K. (2022). Mild solution for the time-fractional Navier–Stokes equation incorporating MHD effects. Fractal and Fractional, 6(10), 580.
• Yokus, A., Kuzu, B. and Demiroglu, U. Investigation of solitary wave solutions for the (3+ 1)-dimensional Zakharov–Kuznetsov equation. International Journal of Modern Physics B, 33(29), 1950350, (2019).
• Yokuş, A., Aydın, M.E., Duran, S. and Durur, H. Simulation of hyperbolic type solitary waves based on velocity parameter for (3+1)-dimensional the B-type Kadomtsev–Petviashvili–Boussinesq equation. Modern Physics Letters B, 36(22), 2250110, (2022).
• Zhou, Q., Xiong, X., Zhu, Q., Liu, Y., Yu, H., Yao, P. et al. Optical solitons with nonlinear dispersion in polynomial law medium. Journal of Optoelectronics and Advanced Materials, 17, 82-86, (2015).
• Zayed, E.M. and Al-Nowehy, A.G. Many new exact solutions to the higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms using three different techniques. Optik, 143, 84-103, (2017).
• Zayed, E.M., Al-Nowehy, A.G. and Elshater, M.E. New-model expansion method and its applications to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity. The European Physical Journal Plus, 133(10), 417, (2018).
• Ozisik, M., Secer, A., Bayram, M., Yusuf, A. and Sulaiman, T.A. On the analytical optical soliton solutions of perturbed Radhakrishnan–Kundu–Lakshmanan model with Kerr law nonlinearity. Optical and Quantum Electronics, 54(6), 371, (2022).
• Atas, S.S., Ali, K.K., Sulaiman, T.A. and Bulut, H. Invariant optical soliton solutions to the Coupled-Higgs equation. Optical and Quantum Electronics, 54(11), 754, (2022).
• Sulaiman, T.A. Three-component coupled nonlinear Schrödinger equation: optical soliton and modulation instability analysis. Physica Scripta, 95(6), 065201, (2020).
• Veeresha, P., Yavuz, M. and Baishya, C. A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(3), 52-67, (2021).
• Younas, U., Bilal, M., Sulaiman, T.A., Ren, J. and Yusuf, A. On the exact soliton solutions and different wave structures to the double dispersive equation. Optical and Quantum Electronics, 54, 1-22, (2022).
• Kudryashov, N.A. Exact solutions of the complex Ginzburg–Landau equation with law of four powers of nonlinearity. Optik, 265, 169548, (2022).
• El-Ganaini, S. and Al-Amr, M.O. New abundant solitary wave structures for a variety of some nonlinear models of surface wave propagation with their geometric interpretations. Mathematical Methods in the Applied Sciences, 45(11), 7200-7226, (2022).
• Farag, N.G., Eltanboly, A.H., El-Azab, M.S. and Obayya, S.S.A. Pseudo-spectral approach for extracting optical solitons of the complex Ginzburg Landau equation with six nonlinearity forms. Optik, 254, 168662, (2022).
• Tarla, S., Ali, K.K. and Yilmazer, R. Newly modified unified auxiliary equation method and its applications. Optik, 269, 169880, (2022).
• Duran, S. Travelling wave solutions and simulation of the Lonngren wave equation for tunnel diode. Optical and Quantum Electronics, 53, 458, (2021).
• Durur, H. Traveling wave solutions of the oskolkov equation arising in incompressible viscoelastic Kelvin–Voigt fluid. Bilecik ¸Seyh Edebali Üniversitesi Fen Bilimleri Dergisi, 9(2), 931-938, (2022).
• Duran, S., Yokuş, A., Durur, H. and Kaya, D. Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics. Modern Physics Letters B, 35(26), 2150363, (2021).
• Aslan, E.C. Solitary solutions and modulation instability analysis of the nonlinear Schrödinger equation with Cubic-Quartic nonlinearity. Journal of Advanced Physics, 6(4), 579-585, (2017).
• Isah, M.A. and Yokuş, A. The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. Mathematical Modelling and Numerical Simulation with Applications, 2(3), 147-163, (2022).
• Abdou, M.A., Soliman, A.A., Biswas, A., Ekici, M., Zhou, Q. and Moshokoa, S.P. Darksingular combo optical solitons with fractional complex Ginzburg-Landau equation. Optik, 171, 463-467, (2018).
• Al-Ghafri, K.S. Soliton behaviours for the conformable space-time fractional complex Ginzburg-Landau equation in optical fibers. Symmetry, 12(2), 219, (2020).
• Biswas, A., Yildirim, Y., Yasar, E., Triki, H., Alshomrani, A.S., Ullah, M.Z. et al. Optical soliton perturbation with complex Ginzburg–Landau equation using trial solution approach. Optik, 160, 44-60, (2018).
• Arshed, S., Biswas, A., Mallawi, F. and Belic, M.R. Optical solitons with complex Ginzburg–Landau equation having three nonlinear forms. Physics Letters A, 383(36), 126026, (2019).
• Li, Z. and Han, T. New exact traveling wave solutions of the time fractional complex GinzburgLandau equation via the conformable fractional derivative. Advances in Mathematical Physics, 2021, 1-12, (2021).
• Arshed, S., Raza, N., Rahman, R.U., Butt, A.R. and Huang, W.H. Sensitive behavior and optical solitons of complex fractional Ginzburg–Landau equation: a comparative paradigm. Results in Physics, 28, 104533, (2021).
• Sajid, N. and Akram, G. Novel solutions of Biswas-Arshed equation by newly φ6-model expansion method. Optik, 211, 164564, (2020).
• Biswas, A. Chirp-free bright optical solitons and conservation laws for complex Ginzburg-Landau equation with three nonlinear forms. Optik 174, 207-215, (2018).