Optical solitons of the coupled nonlinear Schrödinger’s equation with spatiotemporal dispersion. (English) Zbl 1355.35172
Summary: In this work, the coupled nonlinear Schrödinger’s equation (CNLSE) is studied with four forms of nonlinearity. The nonlinearities that are considered in this paper are the Kerr law, power law, parabolic law and dual-power law. Jacobi elliptic function solutions and also bright and dark optical soliton solutions are obtained for each law of the CNLSE. We will acquire constraint conditions for the existence of obtained solitons.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
References:
| [1] | Liang, P., Liang, J.: Jacobi elliptic function solutions to (1+ 1) dimensional nonlinear Schrödinger equation in management system. Optik 122, 1289-1292 (2011) |
| [2] | Miao, X; Zhang, Z, The modified G’/G-expansion method and traveling wave solutions of nonlinear the perturbed nonlinear schrödinger’s equation with Kerr law nonlinearity, Commun. Nonlinear Sci. Numer. Simul., 16, 4259-4267, (2011) · Zbl 1221.35399 · doi:10.1016/j.cnsns.2011.03.032 |
| [3] | Biswas, A, Theory of optical couplers, Opt. Quantum Electron., 35, 221-235, (2003) · doi:10.1023/A:1022852801087 |
| [4] | Mirzazadeh, M; Eslami, M; Zerrad, E; Mahmood, MF; Biswas, A; Belic, M, Optical solitons in nonlinear directional couplers by sine-cosine function method and bernoulli’s equation approach, Nonlinear Dyn., 81, 1933-1949, (2015) · Zbl 1348.78023 · doi:10.1007/s11071-015-2117-y |
| [5] | Biswas, A., Konar, S.: Introduction to Non-Kerr Law Optical Solitons. CRC Press, Boca Raton (2006) · Zbl 1156.78001 · doi:10.1201/9781420011401 |
| [6] | Topkara, E; Milovic, D; Sarma, AK; Zerrad, E; Biswas, A, Optical solitons with non-Kerr law nonlinearity and inter-modal dispersion with time-dependent coefficients, Commun. Nonlinear Sci. Numer. Simul., 15, 2320-2330, (2010) · Zbl 1222.78044 · doi:10.1016/j.cnsns.2009.09.029 |
| [7] | Wazwaz, AM, A study on linear and nonlinear schrodinger equations by the variational iteration method, Chaos Solitons Fractals, 37, 1136-1142, (2008) · Zbl 1148.35353 · doi:10.1016/j.chaos.2006.10.009 |
| [8] | Biswas, A; Milovic, D, Optical solitons with log-law nonlinearity, Commun. Nonlinear Sci. Numer. Simul., 15, 3763-3767, (2010) · Zbl 1222.78037 · doi:10.1016/j.cnsns.2010.01.022 |
| [9] | Ablowitz, M.J.: Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, New York (1991) · Zbl 0762.35001 · doi:10.1017/CBO9780511623998 |
| [10] | Eslami, M; Mirzazadeh, M, Optical solitons with biswas-milovic equation for power law and dual-power law nonlinearities, Nonlinear Dyn., 83, 731-738, (2016) · Zbl 1349.78053 · doi:10.1007/s11071-015-2361-1 |
| [11] | Biswas, A; Khalique, CM, Stationary solutions for nonlinear dispersive schrödinger’s equation, Nonlinear Dyn., 63, 623-626, (2011) · doi:10.1007/s11071-010-9824-1 |
| [12] | Zhou, Q; Liu, S, Dark optical solitons in quadratic nonlinear media with spatio-temporal dispersion, Nonlinear Dyn., 81, 733-738, (2015) · Zbl 1431.35187 · doi:10.1007/s11071-015-2023-3 |
| [13] | Jiang, Y; Tian, B; Li, M; Wang, P, Bright hump solitons for the higher-order nonlinear Schrödinger equation in optical fibers, Nonlinear Dyn., 74, 1053-1063, (2013) · Zbl 1284.35401 · doi:10.1007/s11071-013-1023-4 |
| [14] | Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami M.: Optical solitons with Biswas-Milovic equation by extended trial equation method. Nonlinear Dyn. (2016). doi:10.1007/s11071-016-2613-8 (in press) · Zbl 1355.78029 |
| [15] | Mirzazadeh, M; Arnous, AH; Mahmood, MF; Zerrad, E; Biswas, A, Soliton solutions to resonant nonlinear schrödinger’s equation with time-dependent coefficients by trial solution approach, Nonlinear Dyn., 81, 277-282, (2015) · Zbl 1347.35216 · doi:10.1007/s11071-015-1989-1 |
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