Optical solitons, nonlinear self-adjointness and conservation laws for Kundu–Eckhaus equation

Chinese Journal of Physics - Tập 55 - Trang 2341-2355 - 2017
Dumitru Baleanu1,2, Mustafa Inc3, Abdullahi Yusuf3,4, Aliyu Isa Aliyu3,4
1Cankaya University, Department of Mathematics, Öğretmenler Cad. 1406530, Ankara Türkiye
2Institute of Space Sciences, Magurele-Bucharest, Romania
3Firat University, Science Faculty, Department of Mathematics, 23119, Elaziğ Türkiye
4Federal University Dutse, Science Faculty, Department of Mathematics, 7156 Jigawa, Nigeria

Tài liệu tham khảo

Kundu, 1984, Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations, J. Math. Phys., 25, 3433, 10.1063/1.526113 Calogero, 1987, Nonlinear evolution equations, rescalings, model PDES and their integrability. II., Inverse Probl., 3, 229, 10.1088/0266-5611/3/2/008 Eckhaus, 1986, The long-time behaviour for perturbed wave-equations and related problems Levi, 2009, The Kundu–Eckhaus equation and its discretizations, J. Phys. A, 42, 465203, 10.1088/1751-8113/42/46/465203 Clarkson, 1990, Exact solutions of the multidimensional derivative nonlinear Schrödinger equation for many-body systems of criticality, J. Phys. A, 23, 4269, 10.1088/0305-4470/23/19/013 Wang, 2015, Bright and dark soliton solutions and Bäcklund transformation for the Eckhaus–Kundu equation with the cubic-quintic nonlinearity, Appl. Math. Comput., 251, 233 Johnson, 1977, On the modulation of water waves in the neighbourhood of kh 1.363, 357, 131 Kodama, 1985, Optical solitons in a monomode fiber, J. Stat. Phys., 39, 597, 10.1007/BF01008354 Ganji, 2008, Exp-function based solution of nonlinear Radhakrishnan, Kundu and Laskshmanan (RKL) equation, Acta Appl. Math., 104, 201, 10.1007/s10440-008-9252-0 Bekir, 2008, Exact solutions for nonlinear evolution equations using exp-function method, Phys. Lett. A., 372, 1619, 10.1016/j.physleta.2007.10.018 Bekir, 2011, Exact solutions for a class of nonlinear partial differential equations using exp-function method, Int. J. Nonlinear Sci. Numer. Simul., 8, 505 Taghizadeh, 2012, The first-integral method applied to the Eckhaus equation, Appl. Math. Lett., 25, 798, 10.1016/j.aml.2011.10.021 Eslami, 2014, Optical solitons for the resonant nonlinear Schrödingers equation with time-dependent coefficients by the first integral method, Optik-Int, J. Light Electron. Opt., 125, 3107, 10.1016/j.ijleo.2014.01.013 Gao, 2015, Comment on Solitons, Bäcklund transformation, and Lax pair for the (2+1)-dimensional BoitiLeonPempinelli equation for the water waves, J. Math. Phys., 56, 10.1063/1.4906031 Gao, 2015, Bäacklund transformation and shock-wave-type solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid mechanics, Ocean Eng., 96, 245, 10.1016/j.oceaneng.2014.12.017 Zhen, 2015, Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma, Phys. Plasmas, 22, 03230, 10.1063/1.4913668 Sun, 2015, Optical rogue waves associated with the negative coherent coupling in an isotropic medium, Phys. Rev. E., 91, 02320, 10.1103/PhysRevE.91.023205 Wang, 2015, Solitons via an auxiliary function for an inhomogeneous higher order nonlinear Schrödinger equation in optical fiber communications, Nonlinear Dyn., 79, 721, 10.1007/s11071-014-1697-2 Al Qurashi, 2017, Optical and other solitons for the fourth-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity, Superlattices Microstruct., 105, 183, 10.1016/j.spmi.2017.03.022 Yang, 2015, A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application, Adv. Differ. Eq., 2015, 117, 10.1186/s13662-015-0452-4 Kumar, 2016, Optical solitons in nano-fibers with Kundu–Eckhaus equation by lie symmetry analysis, Optoelectron. Adv. Mater. Rapid Commun., 10, 21 Guzman, 2015, Dark and singular solitons of Kundu–Eckhaus equation for optical FIBERS, Optoelectron. Adv. Mater. Rapid Commun., 9, 1353 Sturdevant, 2010, topological 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation with nonlinear dispersion, Mod. Phys. Lett. B, 24, 1825, 10.1142/S0217984910024109 Biswas, 2009, 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation, Phys. Lett. A, 373, 2546, 10.1016/j.physleta.2009.05.010 Savescu, 2017, Embedded solitons and conservation law with χ (2) and χ (3) nonlinear susceptibilities, Acta Phys. Polonica A, 131, 297, 10.12693/APhysPolA.131.297 Ekici, 2017, Nematicons in liquid crystals by extended trial equation method, J. Nonlinear Opt. Phys. Mater., 26, 10.1142/S0218863517500059 Haddouche, 2017, Highly sensitive optical immunosensor for bacteria detection in water, Optoelectron. Adv. Mater. Rapid Commun., 11, 46 Ekici, 2017, Optical solitons with dwdm technology and four-wave mixing by extended trial equation method, Superlattices Microstruct., 107, 254, 10.1016/j.spmi.2017.04.030 Ja'afar, 2017, Optical solitons with anti-cubic nonlinearity using three integration schemes, Superlattices Microstruct., 105 Biswas, 2017, Perturbation theory and optical soliton cooling with anti-cubic nonlinearity, Optik, 142, 73, 10.1016/j.ijleo.2017.05.060 Biswas, 2017, Optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle, Optik, 139, 16, 10.1016/j.ijleo.2017.03.111 Banaja, 2017, The investigation of optical solitons in cascaded system by improved adomian decomposition scheme, Optik, 130, 1107, 10.1016/j.ijleo.2016.11.125 Bakodah, 2017, Bright and dark thirring optical solitons with improved adomian decomposition scheme, Optik, 130, 1115, 10.1016/j.ijleo.2016.11.123 Arnous, 2017, Vematicons in liquid crystals by modified simple equation method, Nonlinear Dyn., 88, 2863, 10.1007/s11071-017-3416-2 Guzman, 2017, Solitons in nonlinear directional couplers with optical metamaterials, Nonlinear Dyn., 87, 427, 10.1007/s11071-016-3052-2 Wang, 2017, Group analysis, nonlinear self-adjointness, conservation laws and soliton solutions for the mkdv systems, Nonlinear Anal., 22, 334, 10.15388/NA.2017.3.4 Kara, 2016, Conservation laws for optical solitons in birefringent fibers and magneto-optic waveguides, Optik, 127, 11662, 10.1016/j.ijleo.2016.09.075 Mirzazadeh, 2016, Optical solitons in birefringent fibers by extended trial equation method, Optik, 127, 11311, 10.1016/j.ijleo.2016.09.058 Ekici, 2016, Optical soliton perturbation with fractional temporal evolution by first integral method with conformable fractional derivatives, Optik, 127, 10659, 10.1016/j.ijleo.2016.08.076 Yanan, 2016, Soliton propagation through nanoscale waveguides in optical metamaterials, Opt. Laser Technol., 77, 177, 10.1016/j.optlastec.2015.08.021 Triki, 2016, Chirped femto-second pulses in higher-order nonlinear schrodinger's equation with non-kerr terms and cubic-quintic-septic nonlinearities, Opt. Commun., 366, 362, 10.1016/j.optcom.2016.01.005 Zhou, 2015, Analytical study of thirring optical solitons with parabolic law nonlinearity and spatio-temporal dispersion, Eur. Phys. J. Plus, 130, 138, 10.1140/epjp/i2015-15138-9 Mirzazadeh, 2015, Bifurcation analysis and bright soliton of generalized resonant dispersive nonlinear schrodinger's equation, Optoelectron. Adv. Mater. Rapid Commun., 9, 1342 Mirzazadeh, 2015, Optical solitons in birefringent fibers with riccati equation method, Optoelectron. Adv. Mater. Rapid Commun., 9, 1032 Savescu, 2015, Optical solitons in dwdm system with four-wave mixing, Optoelectron. Adv. Mater. Rapid Commun., 9, 14 Ghany, 2015, Exact travelling wave solutions for stochastic fractional Hirota–Satsuma coupled kdv equations, Chin. J. Phys., 53 Choi, 2017, Soliton solutions for the space-time nonlinear partial differential equations with fractional-orders, Chin. J. Phys., 55, 556, 10.1016/j.cjph.2016.10.019 Khamitova, 2009 Noether, 1918, Invariante variation probleme, Mathematisch-Physikalische Klasse, 2, 235 Ibragimov, 2007, A new conservation laws theorem, J. Math. Anal., 333, 311, 10.1016/j.jmaa.2006.10.078 Ibragimov, 2010, Nonlinear self-adjointness in constructing conservation laws, Arch. ALGA, 7/4, 1 Ibragimov, 2011, Nonlinear self-adjointness in constructing conservation laws, Arch. ALGA, 44 Jabbari, 2010, New exact travelling wave solutions for the kawahara and modified kawahara equation by using modified tanh-coth method, Acta Universitatis Apulensis, 23, 21 Alofi, 2012, Extended Jacobi elliptic function expansion method for nonlinear Benjamin–Bona–Mahony equations, Int. Math. Forum, 7, 2639 Dimas, 2005, SYM: a new symmetry - finding package for mathematica, 64