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New optical solitary waves for unstable Schrödinger equation in nonlinear medium

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper and for the first time, we describe and introduce a new extended direct algebraic method which is a new method for solving nonlinear partial differential equations arising in nonlinear optics and nonlinear science. By applying this method, we have constructed new solitary wave solutions for the unstable Schrödinger equation. A large family of traveling wave type exact solutions covering exponential, generalized trigonometric, rational and generalized hyperbolic functions to this equation is determined. The solutions are expressed in explicit forms.
Czasopismo
Rocznik
Strony
135--150
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, P.R. China
  • Faculty of Engineering Technology, Amol University of Special Modern Technologies , Amol, Iran
  • Department of Mathematics, Çankırı Karatekin University, Çankırı, Turkey
  • Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
  • Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran
  • Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran
Bibliografia
  • [1] MALFLIET W., The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations, Journal of Computational and Applied Mathematics 164–165, 2004, pp. 529–541, DOI: 10.1016/S0377-0427(03)00645-9.
  • [2] WAZWAZ A.M., The tanh method for traveling wave solutions of nonlinear equations, Applied Mathematics and Computation 154(3), 2004, pp. 713–723, DOI: 10.1016/S0096-3003(03)00745-8.
  • [3] EL-WAKIL S.A., ABDOU M.A., New exact travelling wave solutions using modified extended tanh -function method, Chaos, Solitons and Fractals 31(4), 2007, pp. 840–852, DOI: 10.1016/j.chaos.2005.10.032.
  • [4] AL QURASHI M.M., YUSUF A., ALIYU A.I., INC M., Optical and other solitons for the fourth-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity, Superlattices and Microstructures 105, 2017, pp. 183–197, DOI: 10.1016/j.spmi.2017.03.022.
  • [5] ASLAN E.C., TCHIER F., INC M., On optical solitons of the Schrödinger–Hirota equation with power law nonlinearity in optical fibers, Superlattices and Microstructures 105, 2017, pp. 48–55, DOI: 10.1016/j.spmi.2017.03.014.
  • [6] JI-HUAN HE, XU-HONG WU, Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals 30(3), 2006, pp. 700–708, DOI: 10.1016/j.chaos.2006.03.020.
  • [7] JI-HUAN HE, ABDOU M.A., New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals 34(5), 2007, pp. 1421–1429, DOI: 10.1016/j.chaos.2006.05.072.
  • [8] ABDEL-GAWAD H.I., TANTAWY M., ABO ELKHAIR R.E., On the extension of solutions of the real to complex KdV equation and a mechanism for the construction of rogue waves, Waves in Random and Complex Media 26(3), 2016, pp. 397–406, DOI: 10.1080/17455030.2016.1161863.
  • [9] ABDEL-GAWAD H.I., TANTAWY M., On multi-graded-index soliton solutions for the Boussinesq–Burgers equations in optical communications, Optics Communications 384, 2017, pp. 7–10, DOI: 10.1016/ j.optcom.2016.09.064.
  • [10] ABDEL-GAWAD H.I., TANTAWY M., Propagation of high and low graded-index waveguides in an inhomogeneous-dispersive medium, Superlattices and Microstructures 111, 2017, pp. 991–999, DOI: 10.1016/j.spmi.2017.07.061.
  • [11] ABDEL-GAWAD H.I., TANTAWY M., Exact solutions of the Shamel–Korteweg–de Vries equation with time dependent coefficients, Information Sciences Letters 3(3), 2014, pp. 103–109, DOI: 10.12785/ isl/030303.
  • [12] HAFEZ M.G., AKBAR M.A., New exact traveling wave solutions to the (1+1)-dimensional Klein –Gordon–Zakharov equation for wave propagation in plasma using the exp(–Φ(ξ))-expansion method, Propulsion and Power Research 4(1), 2015, pp. 31–39, DOI: 10.1016/j.jppr.2015.02.002.
  • [13] BISWAS A., REZAZADEH H., MIRZAZADEH M., ESLAMI M., EKICI M., QIN ZHOU, MOSHOKOA S.P., BELIC M., Optical soliton perturbation with Fokas-Lenells equation using three exotic and efficient integration schemes, Optik 165, 2018, pp. 288–294, DOI: 10.1016/j.ijleo.2018.03.132.
  • [14] KORKMAZ A., HOSSEINI K., Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods, Optical and Quantum Electronics 49(8), 2017, article ID 278, DOI: 10.1007/s11082-017-1116-2.
  • [15] MANAFIAN J., LAKESTANI M., The classification of the single traveling wave solutions to the modified Fornberg–Whitham equation, International Journal of Applied and Computational Mathematics 3(4), 2017, pp. 3241–3252, DOI: 10.1007/s40819-016-0288-y.
  • [16] REZAZADEH H., MANAFIAN J., KHODADAD F.S., NAZARI F., Traveling wave solutions for density-dependent conformable fractional diffusion–reaction equation by the first integral method and the improved tan(Φ(ξ)/2)-expansion method, Optical and Quantum Electronics 50(3), 2018, article ID 121, DOI: 10.1007/s11082-018-1388-1.
  • [17] MANAFIAN J., Optical soliton solutions for Schrödinger type nonlinear evolution equations by the tan(Φ(ξ)/2)-expansion method, Optik 127(10), 2016, pp. 4222–4245, DOI: 10.1016/j.ijleo.2016.01.078.
  • [18] TALA-TEBUE E., DJOUFACK Z.I., FENDZI-DONFACK E., KENFACK-JIOTSA A., KOFANÉ T.C., Exact solutions of the unstable nonlinear Schrödinger equation with the new Jacobi elliptic function rational expansion method and the exponential rational function method, Optik 127(23), 2016, pp. 11124–11130, DOI: 10.1016/j.ijleo.2016.08.116.
  • [19] DIANCHEN LU, SEADAWY A.R., ARSHAD M., Bright–dark solitary wave and elliptic function solutions of unstable nonlinear Schrödinger equation and their applications, Optical and Quantum Electronics 50(1), 2018, article ID 23, DOI: 10.1007/s11082-017-1294-y.
  • [20] ARSHAD M., SEADAWY A.R., DIANCHEN LU, WANG JUN, Optical soliton solutions of unstable nonlinear Schrödinger dynamical equation and stability analysis with applications, Optik 157, 2018, pp. 597 –605, DOI: 10.1016/j.ijleo.2017.11.129.
  • [21] REZAZADEH H., New solitons solutions of the complex Ginzburg–Landau equation with Kerr law nonlinearity, Optik 167, 2018, pp. 218–227, DOI: 10.1016/j.ijleo.2018.04.026.
  • [22] YUJIE REN, HONGQING ZHANG, New generalized hyperbolic functions and auto-Bäcklund transformation to find new exact solutions of the (2+1)-dimensional NNV equation, Physics Letters A 357(6), 2006, pp. 438–448, DOI: 10.1016/j.physleta.2006.04.082.
  • [23] PANDIR Y., ULUSOY H., New generalized hyperbolic functions to find new exact solutions of the nonlinear partial differential equations, Journal of Mathematics 2013, 2013, article ID 201276, DOI: 10.1155/2013/201276.
  • [24] WENJUN LIU, CHUNYU YANG, MENGLI LIU, WEITIAN YU, YUJIA ZHANG, MING LEI, Effect of high-order dispersion on three-soliton interactions for the variable-coefficients Hirota equation, Physical Review E 96(4), 2017, article ID 042201, DOI: 10.1103/PhysRevE.96.042201.
  • [25] WENJUN LIU, WEITIAN YU, CHUNYU YANG, MENGLI LIU, YUJIA ZHANG, MING LEI, Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers, Nonlinear Dynamics 89(4), 2017, pp. 2933–2939, DOI: 10.1007/s11071-017-3636-5.
  • [26] CHUNYU YANG, WENYI LI, WEITIAN YU, MENGLI LIU, YUJIA ZHANG, GUOLI MA, MING LEI, WENJUN LIU, Amplification, reshaping, fission and annihilation of optical solitons in dispersion-decreasing fiber, Nonlinear Dynamics 92(2), 2018, pp. 203–213, DOI: 10.1007/s11071-018-4049-9.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cfb5080f-ffcf-40b3-ba26-57858576e436
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