880
Views
6
CrossRef citations to date
0
Altmetric
Research Article

Travelling wave solutions and modulation instability analysis of the nonlinear Manakov-system

, , &
Article: 2201967 | Received 17 Jul 2022, Accepted 06 Apr 2023, Published online: 22 Apr 2023

References

  • Yıldırım Y. Optical soliton molecules of Manakov model by trial equation technique. Optik. 2019;185:1146–1151.
  • Ozisik M, Secer A, Bayram M. On the examination of optical soliton pulses of Manakov system with auxiliary equation technique. Optik. 2022;268:169800.
  • Stalin S, Ramakrishnan R, Senthilvelan M, et al. Nondegenerate solitons in Manakov system. Phys Rev Lett. 2019;122:043901.
  • Frisquet B, Kibler B, Fatome J, et al. Polarization modulation instability in a Manakov fiber system. Phys Rev A. 2015;92:053854.
  • Copie F, Randoux S, Suret P. The physics of the one-dimensional nonlinear Schrödinger equation in fiber optics: rogue waves, modulation instability and self-focusing phenomena. Rev Phys. 2020;5:100037.
  • Abdel-Gawad HI, Biswas A, Alshomrani AS, et al. Optical solitons and stability analysis with coupled nonlinear Schrödingers equations having double external potentials. Res Phys. 2019;15:102707.
  • Zhang G, Yan Z, Wen XY, et al. Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations. Phys Rev E. 2017;95(4):042201.
  • Ali K, Seadawy AR, Ahmed S, et al. Discussion on rational solutions for nematicons in liquid crystals with Kerr law. Chaos Solitons Fractals. 2022;160:112218.
  • Rizvi STR, Seadawy AR, Ali K, et al. Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity. Optical Quantum Electron. 2022;54(4):1–14.
  • Seadawy AR, Younis M, Baber MZ, et al. Nonlinear acoustic wave structures to the Zabolotskaya–Khokholov dynamical model. J Geom Phys. 2022;175:104474.
  • Rehman HU, Seadawy AR, Younis M, et al. Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3+1)-dimensional generalized Korteweg–de-Vries–Zakharov–Kuznetsov equation in plasma physics. Res Phys. 2022;33:105069.
  • Akram U, Seadawy AR, Rizvi STR, et al. Applications of the resonanat nonlinear Schrödinger equation with self steeping phenomena for chirped periodic waves. Opt Quantum Electron. 2022;54(4):1–36.
  • Rizvi STR, Ali K, Bekir A, et al. Investigation on the single and multiple dromions for nonlinear telegraph equation in electrical transmission line. Qual Theory Dyn Syst. 2022;21(1):1–14.
  • Rizvi STR, Seadawy AR, Abbas SO, et al. Exact and numerical solutions to the system of the chlorite iodide malonic acid chemical reactions. Comput Appl Math. 2022;41(1):1–18.
  • Seadawy AR, Rizvi STR, Mustafa B, et al. Chirped periodic waves for an cubic-quintic nonlinear Schrödinger equation with self steepening and higher order nonlinearities. Chaos Solitons Fractals. 2022;156:111804.
  • Rizvi STR, Seadawy AR, Akram U, et al. Solitary wave solutions along with painleve analysis for the Ablowitz–Kaup–Newell–Segur water waves equation. Modern Phys Lett B. 2022;36(02):2150548.
  • Rizvi STR, Seadawy A, Akram U. New dispersive optical soliton for an nonlinear Schrödinger equation with Kudryashov law of refractive index along with P-test. Opt Quantum Electron. 2022;54(5):1–23.
  • Alruwaili AD, Seadawy AR, Rizvi STR, et al. Diverse multiple lump analytical solutions for ion sound and Langmuir waves. Mathematics. 2022;10(2):200.
  • Jia HX. Solitons in PT symmetric Manakov system. Optik: Int J Light Election Opt. 2004;230:166223.
  • Ye Y, Liu J, Bu L, et al. Rogue waves and modulation instability in an extended Manakov system. Nonlinear Dyn. 2020;102:1801–1812.
  • Guan WY, Li BQ. Asymmetrical and self-similar structures of optical breathers for the Manakov system in photorefractive crystals and randomly birefringent fibers. Optik: Int J Light Election Opt. 2019;194:162882.
  • Ahmed HM, El-Sheikh MMA, Arnous AHSEP, et al. Construction of the soliton solutions for the Manakov system by extended simplest equation method. Int J Appl Comput Math. 2021;7:239.
  • Ma G, Zhou Q, Yu W, et al. Stable transmission characteristics of double-hump solitons for the coupled Manakov equations in fiber lasers. Nonlinear Dyn. 2021;106:2509–2514.
  • Vijayajayanthi M, Kanna T, Lakshmanan M, et al. Explicit construction of single input–single output logic gates from three soliton solution of Manakov system. Commun Nonlinear Sci Numer Simul. 2016;36:391–401.
  • Wu GZ, Fang Y, Wang YY, et al. Predicting the dynamic process and model parameters of the vector optical solitons in birefringent fibers via the modified PINN. Chaos Solitons Fractals. 2021;152:111393.
  • Stalin S, Ramakrishnan R, Lakshmanan M. Nondegenerate soliton solutions in certain coupled nonlinear Schrödinger systems. Phys Lett A. 2020;384:126201.
  • Ismail MS, Kanna T. Numerical study of bright-bright-dark soliton dynamics in the mixed coupled nonlinear Schrödinger system. Optik: Int J Light Election Opt. 2020;224:165633.
  • Gerdjikov VS, Kostov NA, Doktorov EV, et al. Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures. Math Comput Simul. 2009;80:112–119.
  • Gerdjikov VS, Doktorov EV, Matsuka NP. N-soliton train and generalized complex Toda chain for the Manakov system. Theoret Math Phys. 2007;151(3):762–773.
  • Kraus D, Biondini G, Kovačič G. The focusing Manakov system with nonzero boundary conditions. Nonlinearity. 2015;28(9):3101.
  • Pu JC, Chen Y. Data-driven vector localized waves and parameters discovery for Manakov system using deep learning approach. Chaos Solitons Fractals. 2022;160:112182.
  • Barletti L, Brugnano L, Tang Y, et al. Spectrally accurate space–time solution of Manakov systems. J Comput Appl Math. 2020;377:112918.
  • Raskovalov AA, Gelash AA. Resonance interaction of breathers in the Manakov system. Theoret Math Phys. 2022;213(3):1669–1685.
  • Wang D-S, Zhang D-J, Yang J. Integrable properties of the general coupled nonlinear Schrödinger equations. J Math Phys. 2010;51(2):023510.
  • Ma G, Zhou Q, Yu W, et al. Stable transmission characteristics of double-hump solitons for the coupled Manakov equations in fiber lasers. Nonlinear Dyn. 2021;106(3):2509–2514.
  • Gerdjikov VS, Todorov MD. Manakov model with gain/loss terms and N-soliton interactions: effects of periodic potentials. Appl Numer Math. 2019;141:62–80.
  • Chen S, Zhou R. An integrable decomposition of the Manakov equation. Comput Appl Math. 2012;31:01–18.
  • Frisquet B, Kibler B, Fatome J, et al. Polarization modulation instability in a Manakov fiber system. Phys Rev A. 2015;92(5):053854.
  • Yilmaz EU, Khodad FS, Ozkan YS, et al. Manakov model of coupled NLS equation and its optical soliton solutions. J Ocean Eng Sci. 2022. In press.
  • Mumtaz S, Essiambre R, Agrawal GP. Nonlinear propagation in multimode and multicore fibers: generalization of the Manakov equations. J Lightwave Technol. 2012;31(3):398–406.
  • Hedli R, Kadem A. Exact traveling wave solutions to the fifth-order KdV equation using the exponential expansion method. Int J Appl Math. 2020;50:1.
  • Korkmaz A, Hosseini K. Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Opt Quantum Electron. 2017;49:31.
  • Hafez MG, Akbar MA. An exponential expansion method and its application to the strain wave equation in microstructured solids. Ain Shams Eng J. 2015;6:683–690.
  • Kadkhoda N, Jafari H. Analytical solutions of the Gerdjikov–Ivanov equation by using exp⁡(−ϕ(ξ))-expansion method. Optik: Int J Light Election Opt. 2017;139:72–76.
  • Akram G, Sadaf M, Khan MA. Abundant optical solitons for Lakshmanan–Porsezian–Daniel model by the modified auxiliary equation method. Optik: Int J Light Election Opt. 2022;251:168163.
  • Akram G, Sadaf M, Khan MA. Soliton solutions of Lakshmanan–Porsezian–Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities. Optik: Int J Light Election Opt. 2022;252:168372.
  • Akram G, Gillani SR. Sub pico-second soliton with Triki–Biswas equation by the extended (G′G2)-expansion method and the modified auxiliary equation method. Optik: Int J Light Election Opt. 2021;229:166227.
  • Akbulut A, Kaplan M, Tascan F. The investigation of exact solutions of nonlinear partial differential equations by using exp (- ϕ (ξ)) method. Optik. 2017;132:382–387.
  • Kaplan M, Akbulut A. A novel exploration for traveling wave solutions to the integrable equation of wave packet envelope. Partial Differ Equ Appl Math. 2022;5:100312.
  • Akbulut A, Islam SMR, Rezazadeh H, et al. Obtaining exact solutions of nonlinear partial differential equations via two different methods. Int J Modern Phys B. 2022;36(05):2250041.
  • Xu B, Zhang S. Exact solutions of nonlinear equations in mathematical physics via negative power expansion method. J Math Phys Anal Geo. 2021;17:369–387.
  • Zhang S, Xu B. Painlevé test and exact solutions for (1+1)-dimensional generalized Broer–Kaup equations. Mathematics. 2022;10(3):486.
  • Zhang S. Exact solutions of a KdV equation with variable coefficients via exp-function method. Nonlinear Dyn. 2008;52(1):11–17.
  • Mahmud F, Samsuzzoha M, Akbar MA. The generalized Kudryashov method to obtain exact traveling wave solutions of the PHI-four equation and the fisher equation. Res Phys. 2017;7:4296–4302.
  • Ghazanfar S, Ahmed N, Iqbal MS, et al. Imaging ultrasound propagation using the Westervelt equation by the generalized Kudryashov and modified Kudryashov methods. Appl Sci. 2022;12(22):11813.
  • Ozisik M. Soliton solutions of nonlinear (2+1)-dimensional Biswas–Milovic equation via new approach of generalized Kudryashov scheme. NTMSCI 10 Special Iss. 2022:43(1):47–53.
  • Sirisubtawee S, Koonprasert S. Exact traveling wave solutions of certain nonlinear partial differential equations using the G′G2-expansion method. Adv Math Phys. 2018;2018:7628651.
  • Abdelrahman MAE, Zahran EHM, Khater MMA. The exp (-φ (ξ))-expansion method and its application for solving nonlinear evolution equations. Int J Modern Nonlinear Theory Appl. 2015;4(1):37.