New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method

Kaplan, 2016, Exact solutions of nonlinear Schrödinger equation by using symbolic computation, Math. Methods Appl. Sci., 39, 2093, 10.1002/mma.3626 Lu, 2017, Applications of extended simple equation method on unstable nonlinear Schrödinger equations, Optik, 140, 136, 10.1016/j.ijleo.2017.04.032 Hosseini, 2017, New exact traveling wave solutions of the unstable nonlinear Schrödinger equations, Commun. Theor. Phys., 68, 761, 10.1088/0253-6102/68/6/761 Hosseini, 2018, New optical solitons of cubic-quartic nonlinear Schrödinger equation, Optik, 157, 1101, 10.1016/j.ijleo.2017.11.124 Eslami, 2013, Soliton solutions of the resonant nonlinear Schrödinger equation in optical fibers with time-dependent coefficients by simplest equation approach, J. Mod. Opt., 60, 1627, 10.1080/09500340.2013.850777 Manafian, 2017, Abundant soliton solutions of the resonant nonlinear Schrödinger equation with time-dependent coefficients by ITEM and He's semi-inverse method, Opt. Quant. Electron., 49, 322, 10.1007/s11082-017-1156-7 Biswas, 2017, Resonant optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle, Optik, 145, 18, 10.1016/j.ijleo.2017.07.028 Biswas, 2017, Optical soliton perturbation with anti-cubic nonlinearity by semi-inverse variational principle, Optik, 143, 131, 10.1016/j.ijleo.2017.06.087 Biswas, 2017, Cubic-quartic optical solitons in Kerr and power law media, Optik, 144, 357, 10.1016/j.ijleo.2017.07.008 Biswas, 2017, Resonant 1-soliton solution in anti-cubic nonlinear medium with perturbations, Optik, 145, 14, 10.1016/j.ijleo.2017.07.036 Biswas, 2017, Optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle, Optik, 139, 16, 10.1016/j.ijleo.2017.03.111 Bakodah, 2017, Bright and dark Thirring optical solitons with improved adomian decomposition method, Optik, 130, 1115, 10.1016/j.ijleo.2016.11.123 Ekici, 2017, The analytical study of solitons to the nonlinear Schrödinger equation with resonant nonlinearity, Optik, 130, 378, 10.1016/j.ijleo.2016.10.098 Biswas, 2016, Optical solitons in nano-fibers with spatio-temporal dispersion by trial solution method, Optik, 127, 7250, 10.1016/j.ijleo.2016.05.052 Zhou, 2017, Optical solitons in parity-time-symmetric mixed linear and nonlinear lattice with non-Kerr law nonlinearity, Superlatt. Microstruct., 109, 588, 10.1016/j.spmi.2017.05.049 Zhou, 2016, Bright, dark, and singular solitons in optical fibers with spatio-temporal dispersion and spatially dependent coefficients, J. Mod. Opt., 63, 950, 10.1080/09500340.2015.1111456 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 Zhou, 2015, Thirring optical solitons in birefringent fibers with spatio-temporal dispersion and Kerr law nonlinearity, Laser Phys., 25, 015402, 10.1088/1054-660X/25/1/015402 Zhou, 2015, Bright dark and singular optical solitons in a cascaded system, Laser Phys., 25, 025402, 10.1088/1054-660X/25/2/025402 Zhou, 2016, Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion, Waves Random Complex Media, 26, 204, 10.1080/17455030.2015.1132863 Zhou, 2014, Optical solitons in birefringent fibers with parabolic law nonlinearity, Opt. Appl., 44, 399 Zhou, 2016, Dark and singular optical solitons with competing nonlocal nonlinearities, Opt. Appl., 46, 79 Zhou, 2014, Optical solitons with spatially-dependent coefficients by Lie symmetry, Optoelectron. Adv. Mater. Rapid Commun., 8, 800 Zhou, 2017, Perturbation theory and optical soliton cooling with anti-cubic nonlinearity, Optik, 142, 73, 10.1016/j.ijleo.2017.05.060 Asma, 2015, Optical soliton perturbation with quadratic-cubic nonlinearity by semi-inverse variational principle, Proc. Roman. Acad. Ser. A, 16, 152 Batool, 2017, On the solitary wave dynamics of complex Ginzburg–Landau equation with cubic nonlinearity, Opt. Quant. Electron., 49, 129, 10.1007/s11082-017-0973-z Triki, 2017, New envelope solitons for Gerdjikov–Ivanov model in nonlinear fiber optics, Superlatt. Microstruct., 111, 326, 10.1016/j.spmi.2017.06.046 Biswas, 2018, Chirped optical solitons of Chen–Lee–Liu equation by extended trial equation scheme, Optik, 156, 999, 10.1016/j.ijleo.2017.12.094 Manafian, 2016, Optical soliton solutions for the Gerdjikov–Ivanov model via tanϕ/2-expansion method, Optik, 127, 9603, 10.1016/j.ijleo.2016.07.032 Manafian, 2017, Applications of the ETEM for obtaining optical soliton solutions for the Lakshmana–Porsezian–Daniel model, Eur. Phys. J. Plus, 132, 494, 10.1140/epjp/i2017-11762-7 Guzman, 2017, Optical solitons for Lakshmanan–Porsezian–Daniel model with spatio-temporal dispersion using the method of undetermined coefficients, Optik, 144, 115, 10.1016/j.ijleo.2017.06.102 Biswas, 2017, Chirp-free bright optical solitons for perturbed Gerdjikov–Ivanov equation by semi-inverse variational principle, Optik, 147, 72, 10.1016/j.ijleo.2017.08.019 Houria, 2017, New types of chirped soliton solutions for the Fokas–Lenells equation, Int. J. Numer. Methods Heat Fluid Flow, 27, 1596, 10.1108/HFF-06-2016-0252 Liu, 2017, Analytic solutions for the generalized complex Ginzburg–Landau equation in fiber lasers, Nonlinear Dyn., 9, 2933, 10.1007/s11071-017-3636-5 Nawaz, 2017, Soliton solutions for quintic complex Ginzburg–Landau model, Superlatt. Microstruct., 110, 49, 10.1016/j.spmi.2017.09.006 Arnous, 2017, Optical solitons with complex Ginzburg–Landau equation by modified simple equation method, Optik, 144, 475, 10.1016/j.ijleo.2017.07.013 Demiray, 2015, New soliton solutions for Sasa–Satsuma equation, Waves Random Complex Media, 25, 417, 10.1080/17455030.2015.1042945 Wright, 2007, Sasa–Satsuma equation, unstable plane waves and heteroclinic connections, Chaos Solitons Fract., 33, 374, 10.1016/j.chaos.2006.09.034 Khater, 2017, Dispersive optical soliton solutions for higher order nonlinear Sasa–Satsuma equation in mono mode fibers via new auxiliary equation method, Superlatt. Microstruct. Sulaiman, 2017, Investigation of various soliton solutions to the Heisenberg ferromagnetic spin chain equation, J. Electromagn. Waves Appl. Bulut, 2017, Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation, Superlatt. Microstruct. Kumar, 2018, Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chin. J. Phys., 56, 75, 10.1016/j.cjph.2017.11.020 Khater, 2017, Implementation of three reliable methods for finding the exact solutions of (2+1)-dimensional generalized fractional evolution equations, Opt. Quant. Electron., 49, 427 Kumar, 2017, The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzica type equations in nonlinear optics, Optik, 149, 439, 10.1016/j.ijleo.2017.09.066 Yan, 2001, New explicit solitary wave solutions and periodic wave solutions for Whitham–Broer–Kaup equation in shallow water, Phys. Lett. A, 285, 355, 10.1016/S0375-9601(01)00376-0 Xia, 2001, New explicit and exact travelling wave solutions for a class of nonlinear evolution equations, Appl. Math. Mech., 22, 788, 10.1023/A:1016359118468 Khater, 2018, Optical soliton and rogue wave solutions of the ultrashort femto-second pulses in an optical fiber via two different methods and its applications, Optik, 158, 434, 10.1016/j.ijleo.2017.12.120 Manafian, 2016, Abundant soliton solutions for the Kundu–Eckhaus equation via tanϕ/2-expansion method, Optik, 27, 5543, 10.1016/j.ijleo.2016.03.041 Ekici, 2016, Dark and singular optical solitons with Kundu–Eckhaus equation by extended trial equation method and extended G′G-expansion scheme, Optik, 127, 10490, 10.1016/j.ijleo.2016.08.074 Mirzazadeh, 2018, Optical solitons and conservation law of Kundu–Eckhaus equation, Optik, 154, 551, 10.1016/j.ijleo.2017.10.084 Biswas, 2018, Optical soliton perturbation with full nonlinearity for Kundu–Eckhaus equation by modified simple equation method, Optik, 157, 1376, 10.1016/j.ijleo.2017.12.108 Shehata, 2016, Exact traveling wave solutions for nonlinear evolutions equations, J. Comput. Theor. Nanosci., 13, 534, 10.1166/jctn.2016.4837 Baskonus, 2015, On the complex structures of Kundu–Eckhaus equation via improved Bernoulli sub-equation function method, Waves Random Complex Media, 25, 720, 10.1080/17455030.2015.1080392 Taghizadeh, 2014, Exact travelling wave solutions for some complex nonlinear partial differential equations, Comput. Methods Diff. Equ., 2, 11 Wang, 2015, Bright and dark soliton solutions and Bcklund transformation for the Eckhaus–Kundu equation with the cubic-quintic nonlinearity, Appl. Math. Comput., 251, 233, 10.1016/j.amc.2014.11.014 Taghizadeh, 2012, The first-integral method applied to the Eckhaus equation, Appl. Math. Lett., 25, 798, 10.1016/j.aml.2011.10.021