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Optical and Quantum Electronics

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01-01-2024

Exploration of optical solitons of a hyperbolic nonlinear Schrödinger equation

Authors: Shafiq Ahmad, Shabir Ahmad, Meraj Ali Khan, Aman Ullah

Published in: Optical and Quantum Electronics | Issue 1/2024

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Abstract

The investigation of optical solitons, a subject of significant interest in fibre optics and communications due to its importance in signal transmission and data processing, is the focus of the study. For the (2+1) hyperbolic Schrödinger equation (SE), the main goal is to find novel soliton solutions while taking nonlinear effects into account. The study uses the modified Khater method and sine-Gordon expansion method as two separate techniques to accomplish this goal. The purpose of selecting these techniques is to offer a thorough strategy for finding solutions for the SE. A number of closed-form solutions for the SE can be obtained using Mathematica software, which is one of the study’s important findings. These solutions offer valuable insights into the behavior of optical solitons in complex field.

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Ahmad, S., Salman, A.U., Ahmad, S., Ali, A.: Bright, dark and hybrid multistrip optical soliton solutions of a non-linear Schrödinger equation using modified extended tanh technique with new Riccati solutions. Opt. Quant. Electron. 55(3), 236 (2023a)

Ahmad, S., Hameed, A., Ahmad, S., Ullah, A., Akbar, M.: Stability analysis and some exact solutions of a particular equation from a family of a nonlinear Schrödinger equation with unrestricted dispersion and polynomial nonlinearity. Opt. Quant. Electron. 55(8), 666 (2023b)

Ahmad, J., Mustafa, Z., Turki, N.B., Shah, N.A.: Solitary wave structures for the stochastic Nizhnik–Novikov–Veselov system via modified generalized rational exponential function method. Results Phys. 52, 106776 (2023c)

Ahmad, J., Akram, S., Rehman, S.U., Turki, N.B., Shah, N.A.: Description of soliton and lump solutions to M-truncated stochastic Biswas–Arshed model in optical communication. Results Phys. 51, 106719 (2023d)CrossRef

Ahmed, I., Chunlai, M., Zheng, P.: Exact solution of the(2+1)-dimensional hyperbolic nonlinear Schrödinger equation by adomian decomposition method. Malaya J. Matematik 2(2), 160–4 (2014)CrossRef

Ai-Lin, G., Ji, L.: Exact solutions of (2+1)-dimensional HNLS equation. Commun. Theor. Phys. 54, 401 (2010)MathSciNetCrossRefADS

Apeanti, W.O., Seadawy, A.R., Dianchen, L.: Complex optical solutions and modulation instability of hyperbolic Schrödinger dynamical equation. Results Phys. 12, 2091–2097 (2019)CrossRefADS

Attia, R.A.M., Lu, D., Ak, T., Khater, M.M.A.: Optical wave solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term via modified Khater method. Mod. Phys. Lett. B 34(05), 2050044 (2020)CrossRefADS

Fahim, M.R.A., Kundu, P.R., Islam, M.E., Akbar, M.A., Osman, M.S.: Wave profile analysis of a couple of (3+ 1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach. J. Ocean Eng. Sci. 7(3), 272–279 (2022)CrossRef

Hosseini, K., Sadri, K., Hincal, E., et al.: Periodic and solitary waves of the nonlinear Konno-Oono model: generalized methods. Opt. Quant. Electron. 55, 564 (2023a)CrossRef

Hosseini, K., Hincal, E., Obi, O.A., et al.: Solitary waves of coupled nonlinear Schrödinger equations: a generalized method. Opt. Quant. Electron. 55, 599 (2023b)CrossRef

Hosseini, K., Hinçal, E., Ilie, M.: Bifurcation analysis, chaotic behaviors, sensitivity analysis, and soliton solutions of a generalized Schrödinger equation. Nonlinear Dyn. 111, 17455–17462 (2023c)CrossRef

Islam, M.E., Kundu, P.R., Akbar, M.A., Gepreel, K.A., Alotaibi, H.: Study of the parametric effect of self-control waves of the Nizhnik–Novikov–Veselov equation by the analytical solutions. Results Phys. 22, 103887 (2021)CrossRef

Jawad, A.J., Mohamad: New exact solutions of nonlinear partial differential equations using Tan-Cot function method. Stud. Math. Sci. 5(2), 13–25 (2012)

Khaled K, A., Abdul-Majid, W., Osman, M.S.: Optical soliton solutions to the generalized nonautonomous nonlinear Schrödinger equations in optical fibers via the sine-Gordon expansion method. Optik 208, 164132 (2020)CrossRefADS

Khan, A., Saifullah, S., Ahmad, S., Khan, J., Baleanu, D.: Multiple bifurcation solitons, lumps and rogue waves solutions of a generalized perturbed KdV equation. Nonlinear Dyn. 111(6), 5743–5756 (2023)CrossRef

Khater, M., Anwar, S., Tariq, K.U., Mohamed, M.S.: Some optical soliton solutions to the perturbed nonlinear Schrödinger equation by modified Khater method. AIP Adv. 11(2) (2021)

Kudryashov, N.A.: Traveling wave solutions of the generalized Gerdjikov–Ivanov equation. Optik 219, 165193 (2020)CrossRefADS

Kudryashov, N.A.: Optical solitons of the Schrödinger–Hirota equation of the fourth order. Optik 274, 170587 (2023)CrossRefADS

Kumar, V., Jiwari, R., Djurayevich, A.R., Khudoyberganov, M.U.: Hyperbolic (2+1)-dimensional Schrödinger equation: Similarity analysis, Optimal system and complexitons for the one-parameter group of rotations. Commun. Nonlinear Sci. Numer. Simul. 115, 106784 (2022)CrossRef

Kundu, P.R., Ahamed, Md.R., Fahim, Md.E., Islam, A.M.A.: The sine-Gordon expansion method for higher-dimensional NLEEs and parametric analysis. Heliyon 7(3), (2021)

Li, P., Yuejing, L., Changjin, X., Ren, J.: Insight into Hopf bifurcation and control methods in fractional order BAM neural networks incorporating symmetric structure and delay. Cognit. Comput. 1–43 (2023)

Liu, S., Zhou, Q., Biswas, A., Liu, W.: Phase-shift controlling of three solitons in dispersion-decreasing fibers. Nonlinear Dyn. 98, 395–401 (2019a)CrossRef

Liu, W., Zhang, Y., Luan, Z., Zhou, Q., Mirzazadeh, M., Ekici, M., Biswas, A.: Dromion-like soliton interactions for nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers. Nonlinear Dyn. 96, 729–736 (2019b)CrossRef

Md Ekramul, I., Hemonta Kumar, B., M. Ali, A.: Search for interactions of phenomena described by the coupled Higgs field equation through analytical solutions. Opt. Quant. Electron. 52, 1–19 (2020)

Mua, D., Xub, C., Liua, Z., Panga, Y.: Further insight into bifurcation and hybrid control tactics of a chlorine dioxide-iodine-malonic acid chemical reaction model incorporating delays. MATCH Commun. Math. Comput. Chem. 89(3), 529–566 (2023)CrossRef

Nasreen, N., Dianchen, L., Arshad, M.: Optical soliton solutions of nonlinear Schrödinger equation with second order spatiotemporal dispersion and its modulation instability. Optik 161, 221–229 (2018)CrossRefADS

Ou, W., Xu, C., Cui, Q., Liu, Z., Pang, Y., Farman, M., Ahmad, S., Zeb, A.: Mathematical study on bifurcation dynamics and control mechanism of tri-neuron bidirectional associative memory neural networks including delay. Math. Methods Appl. Sci. (2023)

Purobi Rani, K., Almusawa, H., Md Rezwan Ahamed, F., Md Ekramul, I., M. Ali, A., M. S, O.: Linear and nonlinear effects analysis on wave profiles in optics and quantum physics. Results Phys. 23, 103995 (2021)CrossRef

Rehman, S.U., Ahmad, J.: Diverse optical solitons to nonlinear perturbed Schrödinger equation with quadratic-cubic nonlinearity via two efficient approaches. Phys. Scr. 98(3), 035216 (2023)CrossRefADS

Rehman, S.U., Bilal, M., Ahmad, J.: The study of solitary wave solutions to the time conformable Schrödinger system by a powerful computational technique. Opt. Quant. Electron. 54(4), 228 (2022)CrossRef

Rehman, S.U., Ahmad, J., Muhammad, T.: Dynamics of novel exact soliton solutions to stochastic chiral nonlinear Schrödinger equation. Alex. Eng. J. 79, 568–580 (2023a)CrossRef

Rehman, S.U., Ahmad, J., Muhammad, T.: Dynamics of novel exact soliton solutions to stochastic chiral nonlinear Schrödinger equation. Alex. Eng. J. 79, 568–580 (2023b)CrossRef

Saha, A., Ali, K.K., Rezazadeh, H., Ghatani, Y.: Analytical optical pulses and bifurcation analysis for the traveling optical pulses of the hyperbolic nonlinear Schrödinger equation. Opt. Quant. Electron. 53, 1–19 (2021)CrossRef

Saifullah, S., Fatima, N., Abdelmohsen, S.A.M., Alanazi, M.M., Ahmad, S., Baleanu, D.: Analysis of a conformable generalized geophysical KdV equation with Coriolis effect. Alex. Eng. J. 73, 651–663 (2023)CrossRef

Seadawy, A.R., Kumar, D., Chakrabarty, A.K.: Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method. Eur. Phys. J. Plus 133(5), 182 (2018)CrossRef

Shafqat-ur-Rehman, J. A.: Stability analysis and novel optical pulses to Kundu–Mukherjee–Naskar model in birefringent fibers. Int. J. Mod. Phys. B 2450192 (2023)

Shoukry, I. A. El-G.: The first integral method to the nonlinear schrodinger equations in higher dimensions. In: Abstract and Applied Analysis 2013, Article ID 349173 (2013)

Wang, K.-J., Liu, J.-H.: Diverse optical solitons to the nonlinear Schrödinger equation via two novel techniques. Eur. Phys. J. Plus 138(1), 1–9 (2023)MathSciNetCrossRef

Wazwaz, A.-M., Albalawi, W., El-Tantawy, S.A.: Optical envelope soliton solutions for coupled nonlinear Schrödinger equations applicable to high birefringence fibers. Optik 255, 168673 (2022)CrossRefADS

Xu, C., Cui, X., Li, P., Yan, J., Yao, L.: Exploration on dynamics in a discrete predator-prey competitive model involving feedback controls. J. Biol. Dyn. 17(1), 2220349 (2023a)MathSciNetCrossRefPubMed

Xu, C.J., Cui, Q.Y., Liu, Z.X., Pan, Y.L., Cui, X.H., Ou, W., Rahman, M., Farman, M., Ahmad, S., Zeb, A.: Extended hybrid controller design of bifurcation in a delayed chemostat model. MATCH Commun. Math. Comput. Chem 90(3), 609–648 (2023b)CrossRef

Xu, C., Dan, M., Pan, Y., Aouiti, C., Yao, L.: Exploring bifurcation in a fractional-order predator-prey system with mixed delays. J. Appl. Anal. Comput 13, 1119–1136 (2023c)MathSciNet

Xu, C., Dan, M., Liu, Z., Pang, Y., Aouiti, C., Tunc, O., Ahmad, S., Zeb, A.: Bifurcation dynamics and control mechanism of a fractional-order delayed Brusselator chemical reaction model. Match 89(1), 1–2 (2023d)CrossRef

Yu-Ming, C., Md Rezwan Ahamed, F., Purobi Rani, K., Md Ekramul, I., M. Ali, A., Inc, M.: Extension of the sine-Gordon expansion scheme and parametric effect analysis for higher-dimensional nonlinear evolution equations. J. King Saud Univ. Sci. 33(6), 101515 (2021)CrossRef

Zhou, Q., Zhu, Q.: Optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Waves Random Complex Media 25(1), 52–59 (2015)CrossRefADS

Title: Exploration of optical solitons of a hyperbolic nonlinear Schrödinger equation
Authors: Shafiq Ahmad
Shabir Ahmad
Meraj Ali Khan
Aman Ullah
Publication date: 01-01-2024
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 1/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-05628-5

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