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Soliton sáng và tối trong không gian (n + 1)-chiều với phân tán không thời gian
Tóm tắt
Công trình này nhằm xem xét các giải pháp soliton quang học mới cho phương trình Schrödinger phi tuyến (n + 1)-chiều. Giả thuyết ban đầu được đưa ra dưới dạng các hàm elliptic Jacobi để thu được các soliton quang học tối và sáng trong sự hiện diện của các môi trường không-Kerr khác nhau. Đã sử dụng định luật Kerr, định luật công suất, định luật parabol và định luật công suất kép như các môi trường phi tuyến. Các kết quả thu được là mới mẻ và hữu ích cho sự truyền dẫn của các xung ánh sáng trong sợi quang. Để sự tồn tại của những soliton này, các điều kiện ràng buộc cũng được liệt kê.
Từ khóa
#soliton quang học #phương trình Schrödinger phi tuyến #hàm elliptic Jacobi #môi trường không-Kerr #truyền dẫn ánh sángTài liệu tham khảo
P.D. Green, A. Biswas, Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media. Commun. Nonlinear Sci. Numer. Simul. 15, 3865–3873 (2010)
A. Biswas, 1-Soliton solution of the (1 + 2)-dimensions nonlinear Schrödingers equation in dual-power law media. Phys. Lett. A 372, 5941–5943 (2008)
A. Biswas, Dark solitons for a generalized nonlinear Schrödingers equation with parabolic and dual-power law nonlinearities. Math. Methods Appl. Sci. 3, 958–962 (2011)
T.S. Raju, P.K. Panigrahi, K. Porsezian, Nonlinear compression of solitary waves in asymmetric twin-core fibers. Phys. Rev. E 71, 026608 (2005)
A.A. Alshaery, E.M. Hilal, M.A. Banaja, S.A. Alkhateeb, L. Moraru, A. Biswas, Optical solitons in multiple-core couplers. J. Optoelectron. Adv. Mater. 16, 750–758 (2014)
A. Biswas, D.A. Lott, B. Sutton, K.R. Khan, M.F. Mahmood, Optical gaussons in nonlinear directional couplers. J. Electromagn. Waves Appl. 27, 1976–1985 (2013)
M. Younis, S.T.R. Rizvi, Dispersive dark optical soliton in (2 + 1)-dimensions by \((G^{\prime }/G)\)-expansion with dual-power law nonlinearity. Optik 126, 5812–5814 (2015)
M. Younis, S.T.R. Rizvi, Optical solitons for ultrashort pulses in nano fibers. J. Nanoelectron. Optoelectron. 10, 179–182 (2015)
M. Younis, S.T.R. Rizvi, Q. Zhou, A. Biswas, M. Belic, Optical solitons in dual-core fibers with \(G^{\prime }/G\)-expansion scheme. J. Optoelectron. Adv. Mater. 17, 505–510 (2015)
M. Li, T. Xu, L. Wang, Dynamical behaviors and soliton solutions of a generalized higher-order nonlinear Schrödinger equation in optical fibers. Nonlinear Dyn. 80, 1451–1461 (2015)
Q. Zhou, Analytical solutions and modulational instability analysis to the perturbed nonlinear Schrödinger equation. J. Mod. Opt. 61, 500–503 (2014)
C.M. Khalique, A. Biswas, Optical solitons with dual-power law nonlinearity using lie symmetries. Mod. Phys. Lett. B 24, 1833–1838 (2010)
R. Guo, H.Q. Hao, L.L. Zhang, Optical solitons with dual-power law nonlinearity using lie symmetries. Mod. Phys. Lett. B 27, 1350130–1350140 (2013)
M. Savescu, K.R. Khan, R. Kohl, L. Moraru, A. Yildirim, A. Biswas, Optical soliton perturbation with improved nonlinear Schrödingers equation in nanofibers. J. Nanoelectron. Optoelectron. 8, 208–220 (2013)
A.H. Arnous, M. Mirzazadeh, Q. Zhou, M.F. Mahmood, A. Biswas, M. Belic, Optical solitons with resonant nonlinear Schrdingers equation using \((G^{\prime }/G)\)-expansion scheme. Optoelectron. Adv. Mater. 9, 1214–1220 (2015)
A.H. Arnous, M. Mirzazadeh, S. Moshokoa, S. Medhekar, Q. Zhou, M.F. Mahmood, A. Biswas, M. Belic, Solitons in optical metamaterials with trialsolution approach and Backlund transformation of Riccati equation. J. Comput. Theor. Nanosci. 12, 5940–5948 (2015)
M. Mirzazadeh, M. Eslami, A.H. Arnous, Dark optical solitons of Biswas–Milovic equation with dual-power law nonlinearity. Eur. Phys. J. Plus. https://doi.org/10.1140/epjp/i2015-15004-x
M. Mirzazadeh, A.H. Arnous, M.F. Mahmood, E. Zerrad, A. Biswas, Soliton solutions to resonant nonlinear Schrödingers equation withtime-dependent coefficients by trial solution approach. Nonlinear Dyn. 81, 277–282 (2015)
R.S. Johnson, Anon-linear equation incorporating damping and dispersion. J. Fluid Mech. 42, 49–60 (1970)
W.G. Glöckle, T.F. Nonnenmacher, A fractional calculus approach to self similar protein dynamics. Biophys. J. 68, 46–53 (1995)
M. Younis, S. Ali, Solitary wave and shock wave solitons to the transmission line model for nano-ionic currents along microtubules. Appl. Math. Comput. 246, 460–463 (2014)
J.H. He, Some applications of nonlinear fractional differential equations and their applications. Bull. Sci. Technol. 15, 86–90 (1999)
M. Abdullah, A.R. Butt, N. Raza, A.S. Alshomrani, A.K. Alzahrani, Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives. J. Magn. Magn. Mater. 446, 28–36 (2018)
M. Abdullah, A.R. Butt, N. Raza, E.U. Haque, Semi-analytical technique for the solution of fractional Maxwell fluid. Can. J. Phys. 94, 472–478 (2017)
C. Yang, A.M. Wazwaz, Q. Zhou, W. Liu, Transformation of soliton states for a (2 + 1) dimensional fourth-order nonlinear Schrödinger equation in the Heisenberg ferromagnetic spin chain. Laser Phy. 29, 35401 (2019)
W. Liu, Y. Zhang, H. Triki, M. Mirzazadeh, M. Ekici, Q. Zhou, A. Biswas, M. Belic, Interaction properties of solitonics in inhomogeneous optical fibers. Nonlinear Dyn. 95, 557–563 (2019)
C. Yang, W. Liu, Q. Zhou, D. Mihalache, B.A. Malomed, One-soliton shaping and two-soliton interaction in the fifth-order variable-coefficient nonlinear Schrodinger equation. Nonlinear Dyn. 95, 369–380 (2019)
X. Liu, H. Triki, Q. Zhou, M. Mirzazadeh, W. Liu, A. Biswas, M. Belic, Generation and control of multiple solitons under the influence of parameters. Nonlinear Dyn. 95, 143–150 (2019)
W. Yu, Q. Zhou, M. Mirzazadeh, W. Liu, A. Biswas, Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics. J. Adv. Res. 15, 68–76 (2019)
A. Biswas, M.B. Hubert, M. Justin, G. Betchewe, S.Y. Doka, K.T. Crepin, M. Ekici, Q. Zhou, S.P. Moshokoa, M. Belic, Chirped dispersive bright and singular optical solitons with Schrödinger–Hirota equation. Optik 168, 192–195 (2018)
A. Biswas, Y. Yildirim, E. Yasar, Q. Zhou, S.P. Moshokoa, M. Belic, Sub pico-second pulses in mono-mode optical fibers with Kaup–Newell equation by a couple of integration schemes. Optik 167, 121–128 (2018)
A. Biswas, H. Rezazadeh, M. Mirzazadeh, M. Eslami, M. Ekici, Q. Zhou, S.P. Moshokoa, M. Belic, Optical soliton perturbation with Fokas–Lenells equation using three exotic and efficient integration schemes. Optik 165, 288–294 (2018)
H. Guo, X. Zhang, G. Ma, X. Zhang, C. Yang, Q. Zhou, W. Liu, Analytic study on interactions of some types of solitary waves. Optik 164, 132–137 (2018)
W. Yu, M. Ekici, M. Mirzazadeh, Q. Zhou, W. Liu, Periodic oscillations of dark solitons in nonlinear optics. Optik 165, 341–344 (2018)
N. Raza, S. Sial, M. Kaplan, Exact periodic and explicit solutions of higher dimensional equations with fractional temporal evolution. Optik 156, 628–634 (2018)
N. Raza, M. Abdullah, A.R. Butt, Analytical soliton solutions of BiswasMilovic equation in Kerr and non-Kerr law media. Optik 157, 993–1002 (2018)
N. Raza, A. Javid, Optical dark and singular solitons to the Biswas–Milovic equation in nonlinear optics with spatio-temporal dispersion. Optik 158, 1049–1057 (2018)
B. Younas, M. Younis, M.O. Ahmed, S.T.R. Rizvi, Exact optical solitons in (\(n+1\))-dimensions under anti-cubic law of nonlinearity. Optik 156, 479–486 (2018)
N. Raza, A. Zubair, Optical dark and singular solitons of generalized nonlinear Schrodinger’s equation with anti-cubic law of nonlinearity 65, 1950158 (2019)
M. Younis, Optical solitons in (\(n+1\)) dimensions with Kerr and power law nonlinearities. Mod. Phy. Lett. B 31, 1750186 (2017). (9–pages)
M.M.A. Qurashi, E. Ates, M. Inc, Optical solitons in multiple-core couplers with the nearest neighbors linear coupling. Optik 142, 343–353 (2017)
N. Raza, A. Zubair, Bright, dark and dark-singular soliton solutions of nonlinear Schrodinger’s equation with spatio-temporal dispersion. J. Mod. Opt. 65, 1975–1982 (2018)