Investigating phase portraits and extraction of new solitary wave solutions related to the generalized resonant nonlinear Schrödinger equation
DOI:
https://doi.org/10.31349/RevMexFis.71.031301Keywords:
Resonant nonlinear Schrödinger equation; solitary waves; optical solitons; extended direct algebraic methodAbstract
This research dissects solitary wave solutions of generalized resonant nonlinear Schrödinger equation, whose primary uses include the transmission of light across nonlinear optical fibers. To generate bright, dark, kink-type, and singular kink-type solitary waves that rely on the intensity of the propagating pulse, an extended direct algebraic technique with symbolic computation is used. For different values of the parameters, the propagation of some specific solutions in a graphically detailed report has also been demonstrated. Then the bifurcation structures of the heeded model have been determined using a planer dynamical system and phase portraits.
References
H. Jin et al., A hypothetical learning progression for quantifying phenomena in science, Science and Education 28 (2019) 1181, https://doi.org/10.1007/s11191-019-00076-8
J. X. Yao, Y. Y. Guo, and K. Neumann, Towards a hypothetical learning progression of scientific explanation, Asia-Pacific science education 2 (2016) 1, https://doi.org/10.1186/s41029-016-0011-7
A. Hasegawa, Optical solitons in fibers (Springer Science and Business Media, 2013). https://doi.org/10.1007/BFb0041284
A. A. Sukhorukov et al., Spatial optical solitons in waveguide arrays, IEEE Journal of quantum electronics 39 (2003) 31, https://doi.org/10.1109/JQE.2002.806184
C. Spiess et al., Chirped dissipative solitons in driven optical resonators, Optica 8 (2021) 861, https://doi.org/10.1364/OPTICA.419771
P. Kaur, D. Dhawan, and N. Gupta, Review on optical solitons for long haul transmission, Journal of Optical Communications 45 (2023) 1, https://doi.org/10.1515/joc-2023-0093
H. S. Eisenberg et al., Discrete spatial optical solitons in waveguide arrays, Physical Review Letters 81 (1998) 3383, https://doi.org/10.1103/PhysRevLett.81.3383
A. Biswas, Quasi-stationary optical solitons with parabolic law nonlinearity, Optics communications 216 (2003) 427, https://doi.org/10.1016/S0030-4018(02)02309-X
F. Ali et al., Solitonic, quasi-periodic, super nonlinear and chaotic behaviors of a dispersive extended nonlinear Schrödinger equation in an optical fiber, Results in Physics 31 (2021) 104921, https://doi.org/10.1016/j.rinp.2021.104921
N. Raza, S. Arshed, and A. Javid, Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber, International Journal of Nonlinear Sciences and Numerical Simulation 21 (2020) 855, https://doi.org/10.1515/ijnsns-2019-0287
N. Raza et al., Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber, International Journal of Nonlinear Sciences and Numerical Simulation 24 (2021) 1. https://doi.org/10.1515/ijnsns-2021-0165
N. Raza, M. R. Aslam, and H. Rezazadeh, Analytical study of resonant optical solitons with variable coefficients in Kerr and non-Kerr law media, Optical and Quantum Electronics 51 (2019) 1, https://doi.org/10.1007/s11082-019-1773-4
L. Akinyemi et al., Nonlinear dispersion in parabolic law medium and its optical solitons, Results in Physics 26 (2021) 104411, https://doi.org/10.1016/j.rinp.2021.104411
A. Jhangeer, H. Almusawa, and Z. Hussain, Bifurcation study and pattern formation analysis of a non-linear dynamical system for chaotic behavior in travelling wave solution, Results in Physics (2022) 105492, https://doi.org/10.1016/j.rinp.2022.105492
M. Arshad, A. R. Seadawy, and D. Lu, Exact brightdark solitary wave solutions of the higher-order cubicquintic nonlinear Schrödinger equation and its stability, Optik 138 (2017) 40, https://doi.org/10.1016/j.ijleo.2017.03.005
S. Pathania et al., Chirped nonlinear resonant states in femtosecond fiber optics, Optik 227 (2021) 166094, https://doi.org/10.1016/j.ijleo.2020.166094
S. Meradjia et al., Chirped self-similar cnoidal waves and similaritons in an inhomogeneous optical medium with resonant nonlinearity, Chaos Solitons Fractals 141 (2020) 110441, https://doi.org/10.1016/j.chaos.2020.110441
M. Eslami, M. Mirzazadeh, and A. Biswas, Soliton solutions of the resonant nonlinear Schrödinger’s equation in optical fibers with time-dependent coefficients by simplest equation approach, J. Modern Opt. 60 (2013) 1627, https://doi.org/10.1080/09500340.2013.850777
A. R. Seadawy et al., Conservation laws and optical solutions of the resonant nonlinear Schrödinger’s equation with parabolic nonlinearity, Optik 225 (2021) 165762, https://doi.org/10.1016/j.ijleo.2020.165762
H. Triki et al., Bright and dark solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients, Optics and Laser Technology 44 (2012) 2223, https://doi.org/10.1016/j.optlastec.2012.01.037
F. Williams et al., Solitary waves in the resonant nonlinear Schrödinger equation: Stability and dynamical properties, Physics Letters A 22 (2020) 126441, https://doi.org/10.1016/j.physleta.2020.126441
N. A. Kudryashov, Optical solitons of the resonant nonlinear Schrödinger equation with arbitrary index, Optik 235 (2021) 166626, https://doi.org/10.1016/j.ijleo.2021.166626
K. S. Nisar et al., New solutions for the generalized resonant nonlinear Schrödinger equation, Results in Physics 33 (2022) 105153, https://doi.org/10.1016/j.rinp.2021.105153
N. Raza and A. Zubair, Optical dark and singular solitons of generalized nonlinear Schrödinger’s equation with anti-cubic law of nonlinearity, Modern Physics Letters B 33 (2019) 1950158, https://doi.org/10.1142/S0217984919501586
N. Raza and A. Zubair, Bright, dark and dark-singular soliton solutions of nonlinear Schrödinger’s equation with spatiotemporal dispersion, Journal of Modern Optics 65 (2018) 1975, https://doi.org/10.1080/09500340.2018.1480066
N. Raza and Z. A. Alhussain, An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison, Modern Physics Letters B 35 (2021) 2150498, https://doi.org/10.1142/S0217984921504984
A. R. Butt et al., Propagation of novel traveling wave envelopes of Zhiber-Shabat equation by using Lie analysis, International Journal of Geometric Methods in Modern Physics 20 (2023) 2350091, https://doi.org/10.1142/S0219887823500913
C. Liu and Z. Li, The dynamical behavior analysis and the traveling wave solutions of the stochastic SasaSatsuma equation, Qualitative Theory of Dynamical Systems 23 (2024) 157, https://doi.org/10.1007/s12346-024-01022-y
M. S. Ghayad et al., Derivation of optical solitons and other solutions for nonlinear Schrödinger equation using modified extended direct algebraic method, Alexandria Engineering Journal 64 (2023) 801, https://doi.org/10.1016/j.aej.2022.10.054
M. A. Bashir and A. A. Moussa, The cotha (ξ) expansion method and its application to the Davey-Stewartson equation, Applied Mathematical Sciences 8 (2014) 3851, http://dx.doi.org/10.12988/ams.2014.45362
Y. Ren and H. 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 (2006) 438, https://doi.org/10.1016/j.physleta.2006.04.082
S. Thota, An Introduction to Maple software (InNational Conference on Advances in Mathematical sciences, 2012), pp. 05- 07
A. Jhangeer et al., Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model, Pramana 94 (2020) 1, https://doi.org/10.1007/s12043-020-01961-6
N. Raza et al., NDynamical analysis and phase portraits of twomode waves in different media, Results in Physics 19 (2020) 103650, https://doi.org/10.1016/j.rinp.2020.103650
A. Jhangeer et al., New exact solitary wave solutions, bifurcation analysis and first order conserved quantities of resonance nonlinear Schrödinger’s equation with Kerr law nonlinearity, Journal of King Saud University-Science 33 (2021) 101180, https://doi.org/10.1016/j.jksus.2020.09.007
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 A. Rashid Butt, N. Akram, N. Raza
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
