Abstract
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.
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Liang, P., Liang, J.: Jacobi elliptic function solutions to (1+ 1) dimensional nonlinear Schrödinger equation in management system. Optik 122, 1289–1292 (2011)
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)
Biswas, A.: Theory of optical couplers. Opt. Quantum Electron. 35, 221–235 (2003)
Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M.F., 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)
Biswas, A., Konar, S.: Introduction to Non-Kerr Law Optical Solitons. CRC Press, Boca Raton (2006)
Topkara, E., Milovic, D., Sarma, A.K., 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)
Wazwaz, A.M.: A study on linear and nonlinear Schrodinger equations by the variational iteration method. Chaos Solitons Fractals 37, 1136–1142 (2008)
Biswas, A., Milovic, D.: Optical solitons with log-law nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 15, 3763–3767 (2010)
Ablowitz, M.J.: Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, New York (1991)
Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83, 731–738 (2016)
Biswas, A., Khalique, C.M.: Stationary solutions for nonlinear dispersive Schrödinger’s equation. Nonlinear Dyn. 63, 623–626 (2011)
Zhou, Q., Liu, S.: Dark optical solitons in quadratic nonlinear media with spatio-temporal dispersion. Nonlinear Dyn. 81, 733–738 (2015)
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)
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)
Mirzazadeh, M., Arnous, A.H., Mahmood, M.F., 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)
Acknowledgments
This research project was supported by a grant from the “Research Center of the Center for Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University.
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Inc, M., Ates, E. & Tchier, F. Optical solitons of the coupled nonlinear Schrödinger’s equation with spatiotemporal dispersion. Nonlinear Dyn 85, 1319–1329 (2016). https://doi.org/10.1007/s11071-016-2762-9
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DOI: https://doi.org/10.1007/s11071-016-2762-9