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