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Self-phase modulation via similariton solutions of the perturbed NLSE modulation instability and induced self-steepening. (English) Zbl 1511.35318

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
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[1] Poletti, F.; Horak, P., Description of ultrashort pulse propagation in multimode optical fibers, J. Opt. Soc. Am. B, 25, 1645-1654 (2008) · doi:10.1364/JOSAB.25.001645
[2] Mihalache, D.; Torner, L.; Moldoveanu1, F.; Panoiu1, N-C; Truta, N., Soliton solutions for a perturbed nonlinear Schrodinger equation, J. Phys. A, 26, L757 (1993) · Zbl 0802.35140 · doi:10.1088/0305-4470/26/17/001
[3] Sulaiman, T. A.; Bulut, H.; Baskonus, H. M., Optical solitons to the fractional perturbed NLSE in nano fibers, Dis. Cts Dyn. Sys. seies S · Zbl 1437.35650 · doi:10.3934/dcdss.2020054
[4] Mahak, N.; Akram, G., Extension of rational sine-cosine and rational sinh-cosh techniques to extract solutions for the perturbed NLSE with Kerr law nonlinearity, Eur. Phys. J. Plus, 134, 159 (2019) · doi:10.1140/epjp/i2019-12545-x
[5] Malah, M. M.; Ali, H. M.; Ahbar, M. A.; Lai, S., An investigation of abundant traveling wave solutions of complex nonlinear evolution equations: the perturbed nonlinear Schrodinger equation and the cubic-quintic Ginzburg-Landau equation, Cogent Math., 3 (2016) · Zbl 1438.35396 · doi:10.1080/23311835.2016.1277506
[6] Yusuf, A.; Inc, M.; Aliyu, A. I.; Baleanu, D., Beta derivative applied to dark and singular optical solitons for the resonance perturbed NLSE, Eur. Phys. J. Plus, 134, 433 (2019) · doi:10.1140/epjp/i2019-12810-0
[7] Neirmeh, A., New soliton solutions to the fractional perturbed nonlinear Schrodinger equation with power law nonlinearity, SeMA, 73, 309-323 (2016) · Zbl 1369.35086 · doi:10.1007/s40324-016-0070-4
[8] Gsao, W. S.; Ghanbari, B.; Günerhan, H.; H M, Baskonus, Some mixed trigonometric complex soliton solutions to the perturbed nonlinear Schrödinger equation, Mod. Phys. Lett., 34, 03 (2020) · doi:10.1142/S0217984920500347
[9] Zhang, Z-Y; Liu, Z. H.; Miao, X-J; Chen, Y-Z, New exact solutions to the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity, Appl. Math. Comput., 216, 3064-3072 (2010) · Zbl 1195.35283 · doi:10.1016/j.amc.2010.04.026
[10] Zhang, Z-Y; Li, Y-X; Liu, Z-H; Miao, X-J, New exact solutions to the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity via modified trigonometric function series method, Commun. Nonlinear Sci. Numer. Simul., 16, 3097-3106 (2011) · Zbl 1220.65147 · doi:10.1016/j.cnsns.2010.12.010
[11] Zhou, Q., Analytical solutions and modulation instability analysis to the perturbed nonlinear Schrodinger equation, J. Mod. Phys, 61, 500-503 (2014) · Zbl 1356.35231 · doi:10.1080/09500340.2014.897391
[12] Zhang, Z. Y.; Gan, X. Y.; Yu, D. M., Bifurcation behavior of the traveling wave solutions of the perturbed nonlinear Schrodinger’s equation with kerr law nonlinearity, Z Natforsch A, 66, 721-727 (2011) · doi:10.5560/zna.2011-0041
[13] Zhang, Z. Y.; Huang, J.; Zhong, J.; Dou, S. S.; Liu, J.; Peng, D.; Gao, T., The extended -expansion method and traveling wave solutions for the perturbednonlinear Schrödingers equation with Kerr law nonlinearity, Pramana, 82, 1011-1029 (2014) · doi:10.1007/s12043-014-0747-0
[14] Liu, Q. S.; Zhang, Z. Y.; Zhang, R. G.; Huang, C. X., Dynamical analysis and exact solutions of a new (2+1)-dimensional generalized Boussinesq model equation for nonlinear Rossby waves, Commun. Theor. Phys., 71, 1054-1062 (2019) · Zbl 1455.35040 · doi:10.1088/0253-6102/71/9/1054
[15] Alkhidhr, H. A., Closed-form solutions to the perturbed NLSE with Kerr law nonlinearity in optical fibers, Res. Phys., 22 (2021) · doi:10.1016/j.rinp.2021.103875
[16] Bourgain, J., Nonlinear Schrödinger equation with a random potential, Illinois J. Math., 50, 183-188 (2006) · Zbl 1099.37061 · doi:10.1215/ijm/1258059474
[17] Younis, M.; Cheemaa, N.; Mahmood, S. A.; Rizvi, S. T R., On optical solitons: the chiral nonlinear Schrdinger equation with perturbation and Bohm potential, Opt. Quantum Electron., 48, 542 (2016) · doi:10.1007/s11082-016-0809-2
[18] Sulem, C.; Sulem, P. L., The Nonlinear Schrödinger Equation Self-Focusing and Wave Collapse (1999), New-York: Springer, New-York · Zbl 0928.35157
[19] Wazwaz, A. M., Bright and dark optical solitons for (2+1)-dimensional Schrödinger (NLS) equations in the anomalous dispersion regimes and the normal dispersive regimes, Optik, 192 (2019) · doi:10.1016/j.ijleo.2019.162948
[20] Kibler B, B.; Fatome, J.; Finot, C.; Millot, G.; Dias, F.; Genty, G.; Akhmediev, N.; Dudley, J. M., The Peregrine soliton in nonlinear fibre optics, Nat. Phys., 6, 795-797 (2010) · doi:10.1038/nphys1740
[21] Ekici, M.; Sonmezoglua, A.; Biswas, A.; Belic, M. R., Optical solitons in (2+1)-dimensions with Kundu-Mukherjee-Naskar equation by extended trial function scheme, Chin. J. Phys., 57, 72-77 (2019) · Zbl 07808827 · doi:10.1016/j.cjph.2018.12.011
[22] Ma, Y.; Geng, X., A coupled nonlinear Schrödinger type equation and its explicit solutions, Chaos Solitons Fractals, 42, 2949-2953 (2009) · Zbl 1198.37093 · doi:10.1016/j.chaos.2009.04.037
[23] Ahmed, N.; Irshad, A.; Mohyud-Din, S. T.; Khan, U., Exact solutions of perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity by improved \(####\)-expansion method, Opt. Quantum Electron., 50, 45 (2018) · doi:10.1007/s11082-017-1314-y
[24] Eslami, M., Solitary wave solutions for perturbed equation nonlinear Schrödinger’s with Kerr law nonlinearity under the DAM, Optik, 126, 1312-1317 (2015) · doi:10.1016/j.ijleo.2015.02.075
[25] Moosaei, H.; Mirzazadeh, M.; Yildirim, A., Exact solutions to the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity by using the first integral method, Nonlinear Anal. Modelling Control, 16, 332-339 (2011) · Zbl 1276.35051 · doi:10.15388/NA.16.3.14096
[26] Gawad HI, H. I.; Elazab, N. S.; Osman, M., Exact solutions of space dependent Korteweg-de Vries equation by the extended unified method, J. Phys. Soc. Jpn, 82 (2013) · doi:10.7566/JPSJ.82.044004
[27] Abdel-Gawad, H. I., Towards a unified method for exact Solutions of evolution Equations. An application to reaction diffusion equations with finite memory transport, J. Stat. Phys., 147, 506-521 (2012) · Zbl 1362.35070 · doi:10.1007/s10955-012-0467-0
[28] Abdel-Gawad, H. I., Solutions of the generalized transient stimulated Raman scattering equation. Optical pulses compression, Optik, 230 (2021) · doi:10.1016/j.ijleo.2021.166314
[29] Srivastava, H. M.; Abdel-Gawad, H. I.; Saad, K. M., Stability of traveling waves based upon the Evans function and Legendre polynomials, Appl. Sci., 10, 846 (2020) · doi:10.3390/app10030846
[30] Abdel-Gawad, H. I.; Park, H. I C., Interactions of pulses produced by two- mode resonant nonlinear schrodinger equations, Res. Phys., 24 (2021) · doi:10.1016/j.rinp.2021.104113
[31] Abdel-Gawad, H. I.; Tantawy, M.; Fahmy, E. S.; Park, C., Langmuir waves trapping in a (1+ 2) dimensional plasma system. Spectral and modulation stability analysis, Chin. J. Phys., 77, 2148-2159 (2022) · doi:10.1016/j.cjph.2022.01.018
[32] Abdel-Gawad, H. I.; Tantawy, M.; Nkomom, T. N.; Okaly, J. B., On the dynamics of DNA molecules with an-harmonics potential in the normal and damaged states, Phys. Scr., 96 (2021) · doi:10.1088/1402-4896/ac326b
[33] Kodama, Y., Optical solitons in a monomode fiber, J. Stat. Phys., 39, 597-614 (1985) · doi:10.1007/BF01008354
[34] Kodama, Y.; Hasegawa, A., Nonlinear pulse propagation in a monomode dielectric guide, IEEE J. Quantum Electron., 23, 510-524 (1987) · doi:10.1109/JQE.1987.1073392
[35] Zhou, Q.; Wang, T.; Biswas, A.; Liu, W., Nonlinear control of logic structure of all-optical logic devices using soliton interactions, Nonlinear Dyn., 107, 1215-1222 (2022) · doi:10.1007/s11071-021-07027-5
[36] Zhou, Q., Influence of parameters of optical fibers on optical soliton interactions, chinese, Phys. Lett., 39 (2022) · doi:10.1088/0256-307X/39/1/010501
[37] Liua, X.; H Zhang; Liu, W., The dynamic characteristics of pure-quartic solitons and soliton molecules, Appl. Math. Modelling, 102, 305-312 (2022) · Zbl 1525.37080 · doi:10.1016/j.apm.2021.09.042
[38] Ma, G.; Zhao, J.; Zhou, Q.; Biswas, A.; Liu, W., Soliton interaction control through dispersion and nonlinear effects for the fifth-order nonlinear Schrödinger equation, Nonlinear Dyn., 106, 2479-2484 (2021) · doi:10.1007/s11071-021-06915-0
[39] Wang, L-L; Liu, W-J, Stable soliton propagation in a coupled (2 + 1) dimensional Ginzburg-Landau system, Chin. Phys. B, 29 (2020) · doi:10.1088/1674-1056/ab90ea
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