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N. Kudryashov, D. Safonova, A. Biswas (2019)
Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan — Kundu — Lakshmanan EquationRegular and Chaotic Dynamics, 24
A. Biswas, D. Milovic (2010)
Bright and dark solitons of the generalized nonlinear Schrödinger’s equationCommunications in Nonlinear Science and Numerical Simulation, 15
H. Triki, Qin Zhou, S. Moshokoa, M. Ullah, A. Biswas, M. Belić (2018)
Chirped w-shaped optical solitons of Chen–Lee–Liu equationOptik, 155
N. Kudryashov (2019)
A generalized model for description of propagation pulses in optical fiberOptik
N. Kudryashov (2019)
First integrals and general solution of the Fokas–Lenells equationOptik
N. Kudryashov (2019)
Exact solutions of the equation for surface waves in a convecting fluidAppl. Math. Comput., 344-345
N. Kudryashov (2020)
First integrals and general solutions of the Biswas-Milovic equationOptik, 210
H. Triki, Y. Hamaizi, Qin Zhou, A. Biswas, M. Ullah, S. Moshokoa, M. Belić (2017)
Chirped singular solitons for Chen-Lee-Liu equation in optical fibers and PCFOptik, 149
E. Zayed, M. Alngar, A. Biswas, M. Ekici, A. Alzahrani, M. Belic (2020)
Chirped and Chirp-Free Optical Solitons in Fiber Bragg Gratings with Kudryashov’s Model in Presence of Dispersive ReflectivityJournal of Communications Technology and Electronics, 65
Jian-Bing 张, Ying-Yin 公, Shou-Ting 陈 (2017)
Soliton Solutions to the Coupled Gerdjikov–Ivanov Equation with Rogue-Wave-Like PhenomenaChinese Physics Letters, 34
H. Triki, A. Biswas (2018)
Sub pico-second chirped envelope solitons and conservation laws in monomode optical fibers for a new derivative nonlinear Schrödinger's modelOptik
N. Kudryashov (2020)
Mathematical model of propagation pulse in optical fiber with power nonlinearitiesOptik, 212
A. Biswas, S. Arshed (2018)
Optical solitons in presence of higher order dispersions and absence of self-phase modulationOptik
N. Kudryashov (2020)
Solitary wave solutions of hierarchy with non-local nonlinearityAppl. Math. Lett., 103
N. Kudryashov (2019)
Traveling wave solutions of the generalized nonlinear Schrödinger equation with cubic-quintic nonlinearityOptik
Chun-yan Wang (2018)
The analytic solutions of Schrödinger equation with Cubic-Quintic nonlinearitiesResults in Physics
Y. Yıldırım, A. Biswas, M. Ekici, E. Zayed, A. Alzahrani, M. Belić (2021)
Optical soliton perturbation, with maximum intensity, having generalized Kudryashov's law of refractive indexOptik, 227
A. Biswas (2018)
Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesisOptik
M. Ekici, A. Sonmezoglu, A. Biswas, M. Belić (2019)
Optical solitons in (2+1)–Dimensions with Kundu–Mukherjee–Naskar equation by extended trial function schemeChinese Journal of Physics
A. Biswas (2009)
1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equationPhysics Letters A, 373
J. Christian, G. McDonald, A. Kotsampaseris (2018)
Relativistic and pseudorelativistic formulation of nonlinear envelope equations with spatiotemporal dispersion. I. Cubic-quintic systemsPhysical Review A
A. Biswas, M. Ekici, A. Sonmezoglu, M. Belić (2019)
Highly dispersive optical solitons with non-local nonlinearity by F-expansionOptik
Lijuan Guo, Yongshuai Zhang, Shuwei Xu, Zhiwei Wu, Jingsong He (2013)
The higher order rogue wave solutions of the Gerdjikov–Ivanov equationPhysica Scripta, 89
Prakash Das (2019)
The rapidly convergent approximation method to solve system of equations and its application to the Biswas-Arshed equationOptik
E. Zayed, R. Shohib, A. Biswas, M. Ekici, H. Triki, A. Alzahrani, M. Belić (2020)
Optical solitons and other solutions to Kudryashov’s equation with three innovative integration normsOptik
N. Kudryashov (2020)
Traveling wave solutions of the generalized Gerdjikov–Ivanov equationOptik, 219
E. Krishnan, A. Biswas, Qin Zhou, Mohanad Alfiras (2019)
Optical soliton perturbation with Fokas–Lenells equation by mapping methodsOptik
A. Kundu, A. Mukherjee, T. Naskar (2012)
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currentsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470
Qin Zhou, M. Ekici, A. Sonmezoglu, M. Mirzazadeh, M. Eslami (2016)
Analytical study of solitons to Biswas–Milovic model in nonlinear opticsJournal of Modern Optics, 63
E. Zayed, M. Alngar (2020)
Optical soliton solutions for the generalized Kudryashov equation of propagation pulse in optical fiber with power nonlinearities by three integration algorithmsMathematical Methods in the Applied Sciences, 44
N. Kudryashov (2020)
Method for finding highly dispersive optical solitons of nonlinear differential equationsOptik, 206
H. Rehman, M. Saleem, M. Zubair, Sobia Jafar, Iqra Latif (2019)
Optical solitons with Biswas–Arshed model using mapping methodOptik
E. Zayed, M. Alngar, A. Biswas, M. Asma, M. Ekici, A. Alzahrani, M. Belić (2020)
Solitons in magneto–optic waveguides with Kudryashov’s law of refractive indexChaos Solitons & Fractals, 140
Qin Zhou, M. Ekici, A. Sonmezoglu, M. Mirzazadeh, M. Eslami (2016)
Optical solitons with Biswas–Milovic equation by extended trial equation methodNonlinear Dynamics, 84
N. Kudryashov, M. Chmykhov (2014)
Logistic function as solution of many nonlinear differential equationsarXiv: Exactly Solvable and Integrable Systems
N. Kudryashov (2019)
General solution of traveling wave reduction for the Kundu–Mukherjee–Naskar modelOptik
A. Biswas, Y. Yıldırım, E. Yaşar, Qin Zhou, S. Moshokoa, M. Belić (2018)
Optical soliton solutions to Fokas-lenells equation using some different methodsOptik
Y. Yıldırım (2019)
Optical solitons to Kundu–Mukherjee–Naskar model with modified simple equation approachOptik
N. Kudryashov (2020)
First integrals and general solution of the complex Ginzburg-Landau equationAppl. Math. Comput., 386
N. Kudryashov (2020)
Solitary wave solutions of the generalized Biswas-Arshed equationOptik, 219
J. Lenells, A. Fokas (2008)
An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitonsInverse Problems, 25
N. Kudryashov (2004)
Simplest equation method to look for exact solutions of nonlinear differential equationsChaos Solitons & Fractals, 24
N. Kudryashov, E. Antonova (2020)
Solitary waves of equation for propagation pulse with power nonlinearitiesOptik, 217
E. Zayed, M. Alngar, M. El–Horbaty, A. Biswas, A. Alshomrani, M. Ekici, Y. Yıldırım, M. Belić (2020)
Optical solitons with complex Ginzburg-Landau equation having a plethora of nonlinear forms with a couple of improved integration normsOptik, 207
N. Kudryashov (2019)
Construction of nonlinear differential equations for description of propagation pulses in optical fiberOptik
Yuanyuan Yan, Wenjun Liu, Qin Zhou, A. Biswas (2019)
Dromion-like structures and periodic wave solutions for variable-coefficients complex cubic–quintic Ginzburg–Landau equation influenced by higher-order effects and nonlinear gainNonlinear Dynamics, 99
A. Das, A. Biswas, M. Ekici, Qin Zhou, A. Alshomrani, M. Belić (2019)
Optical solitons with complex Ginzburg–Landau equation for two nonlinear forms using F-expansionChinese Journal of Physics
Jianming Zhang, Shuming Li, H. Geng (2016)
Bifurcations of exact travelling wave solutions for the generalized R-K-L equationJournal of Applied Analysis and Computation, 6
Yingying Xie, Zhaoyu Yang, Lingfei Li (2018)
New exact solutions to the high dispersive cubic–quintic nonlinear Schrödinger equationPhysics Letters A
H. Triki, Y. Hamaizi, Qin Zhou, A. Biswas, M. Ullah, S. Moshokoa, M. Belić (2018)
Chirped dark and gray solitons for Chen–Lee–Liu equation in optical fibers and PCFOptik, 155
Qin Zhou, M. Ekici, A. Sonmezoglu (2019)
Exact chirped singular soliton solutions of Triki-Biswas equationOptik
N. Kudryashov (2019)
First integrals and solutions of the traveling wave reduction for the Triki–Biswas equationOptik
N. Kudryashov (2019)
General solution of the traveling wave reduction for the perturbed Chen-Lee-Liu equationOptik
A. Biswas, M. Ekici, A. Sonmezoglu, M. Belić (2019)
Highly dispersive optical solitons with non-local nonlinearity by extended Jacobi's elliptic function expansionOptik
V. Gerdjikov, M. Ivanov (1992)
Expansions over the 'squared' solutions and the inhomogeneous nonlinear Schrodinger equationInverse Problems, 8
E. Zayed, M. Alngar (2020)
Optical soliton solutions for the generalized Kudryashov's equation of propagation pulse in optical fiber with power nonlinearities by three integration algorithms
A nonlinear fourth-order differential equation with arbitrary refractive index for description of the pulse propagation in an optical fiber is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for solutions of the equation using the traveling wave reduction. We present a novel method for finding soliton solutions of nonlinear evolution equations. The essence of this method is based on the hypothesis about the possible type of an auxiliary equation with an already known solution. This new auxiliary equation is used as a basic equation to look for soliton solutions of the original equation. We have found three forms of soliton solutions of the equation at some constraints on parameters of the equation.
Regular and Chaotic Dynamics – Springer Journals
Published: Dec 7, 2020
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