Abstract
This paper addresses soliton propagation through optical fibers by the aid of Biswas–Milovic equation that serves as a generalized version of the usual nonlinear Schrodinger’s equation. Several integration schemes are implemented to secure solitons and other solutions to the model. There are two types of nonlinear media that are studied. They are power law and dual-power law so that Kerr law and parabolic law emerge as special cases to these two laws.
Similar content being viewed by others
References
Biswas, A., Milovic, D.: Bright and dark solitons of the generalized nonlinear Schrödinger’s equation. Commun. Nonlin. Sci. Numer. Simul. 15(6), 1473–1484 (2010)
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. Nonlin. Sci. Numer. Simul. 15(9), 2320–2330 (2010)
Majid, F.: 1-Soliton solution of the Biswas–Milovic equation with log law nonlinearity. Casp. J. Math. Sci. 1(2), 88–93 (2012)
Sturdevant, B.: Topological 1-soliton solution of the Biswas–Milovic equation with power law nonlinearity. Nonlin. Anal. R. World Appl. 11(4), 2871–2874 (2010)
Kohl, R., Tinaztepe, R., Chowdhury, A.: Soliton perturbation theory of Biswas–Milovic equation. Optik 125(8), 1926–1936 (2014)
Triki, H., Biswas, A.: Dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual-power law nonlinearities. Math. Methods Appl. Sci. 34, 958–962 (2011)
Mirzazadeh, M., Eslami, M., Arnous, A.H.: Dark optical solitons of Biswas–Milovic equation with dual-power law nonlinearity. Eur. Phys. J. Plus 130(4), 1–7 (2015)
Manafian, J., Lakestani, M.: Optical solitons with Biswas–Milovic equation for Kerr law nonlinearity. Eur. Phys. J. Plus 130(61), 1–12 (2015)
Crutcher, S.H., Osei, A.: The modulated spatial Gausson solution to the Biswas–Milovic equation with log law nonlinearity. Optik 124(20), 4678–4681 (2013)
Ahmed, I., Chunlai, M., Zhang, F.: Exact solution of the Biswas–Milovic equation by Adomian decomposition method. Int. J. Appl. Math. Res. 2(4), 418–422 (2013)
Zhou, Q., Yao, D., Chen, F.: Analytical study of optical solitons in media with Kerr and parabolic-law nonlinearities. J. Mod. Opt. 60(19), 1652–1657 (2013)
Zhou, Q., Yao, D., Liu, X., Ding, S., Zhang, Y., Chen, F.: Exact solitons in three-dimensional weakly nonlocal nonlinear time-modulated parabolic law media. Opt. Laser Technol. 51, 32–35 (2013)
Zhou, Q.: Analytic study on solitons in the nonlinear fibers with time-modulated parabolic law nonlinearity and Raman effect. Optik 125(13), 3142–3144 (2014)
Safdar, A., Rizvi, S.T.R., Younis, M.: Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients. Nonlin. Dyn. 3(1), 77–79 (2014)
Younis, M., Ali, S., Mahmood, S.A.: Solitons for compound KdV–Burgers equation with variable coefficients and power law nonlinearity. Nonlin. Dyn. 81(3), 1191–1196 (2015)
Zhou, Q., Liu, S.: Dark optical solitons in quadratic nonlinear media with spatio-temporal dispersion. Nonlin. Dyn. 81(1–2), 733–738 (2015)
Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion. Nonlin. Dyn. 80(3), 1365–1371 (2015)
Zhou, Q., Zhu, Q., Yu, H., Xiong, X.: Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion. Nonlin. Dyn. 80(1–2), 983–987 (2015)
Biswas, A., Konar, S.: Introduction to Non-Kerr Law Optical Solitons. CRC Press, Boca Raton (2007)
Biswas, A.: Quasi-stationary non-Kerr law optical solitons. Opt. Fiber Technol. 9(4), 224–259 (2003)
Antonova, M., Biswas, A.: Adiabatic parameter dynamics of perturbed solitary waves. Commun. Nonlin. Sci. Numer. Simul. 14(3), 734–748 (2009)
Biswas, A.: 1-Soliton solution of (1 + 2)-dimensional nonlinear Schrödinger’s equation in dual-power law media. Phys. Lett. A 372(38), 5941–5943 (2008)
Savescu, M., Khan, K.R., Kohl, R.W., Moraru, L., Yildirim, A., Biswas, A.: Optical soliton perturbation with improved nonlinear Schrödinger’s equation in nano fibers. J. Nanoelectron. Optoelectron. 8(2), 208–220 (2013)
Biswas, A.: Topological 1-soliton solution of the nonlinear Schrödinger’s equation with Kerr law nonlinearity in \(1 + 2\) dimensions. Commun. Nonlin. Sci. Numer. Simul. 14(7), 2845–2847 (2009)
Biswas, A.: Perturbation of solitons with non-Kerr law nonlinearity. Chaos Solitons Fractals 13(4), 815–823 (2002)
Kohl, R., Milovic, D., Zerrad, E., Biswas, A.: Soliton perturbation theory for dispersion-managed optical fibers. J. Nonlin. Opt. Phys. Mater. 18(2), 227–270 (2009)
Wazwaz, A.M.: The sine–cosine method for obtaining solutions with compact and noncompact structures. Appl. Math. Comput. 159(2), 559–576 (2004)
Wazwaz, A.M.: A sine–cosine method for handling nonlinear wave equations. Math. Comput. Model. 40(5–6), 499–508 (2004)
Mirzazadeh, M., Eslami, M.: Exact solutions for nonlinear variants of Kadomtsev–Petviashvili \((n, n)\) equation using functional variable method. Pramana J. Phys. 81(6), 911–924 (2013)
Wang, M.L., Li, X.Z., Zhang, J.L.: The \(G^{\prime }/G\)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372(4), 417–423 (2008)
Zayed, E., Gepreel, K.A.: Some applications of the \(G^{\prime }/G\)-expansion method to non-linear partial differential equations. Appl. Math. Comput. 212(1), 1–13 (2009)
Zhang, S., Tong, J.L., Wang, W.: A generalized \(G^{\prime }/G\)-expansion method for the mKdV equation with variable coefficients. Phys. Lett. A 372(13), 2254–2257 (2008)
Kudryashov, N.A.: Exact soliton solutions of the generalized evolution equation of wave dynamics. J. Appl. Math. Mech. 52, 361–365 (1988)
Kudryashov, N.A.: On one of methods for finding exact solutions of nonlinear differential equations. Commun. Nonlin. Sci. Numer. Simul. 17, 2248–2256 (2012)
Kudryashov, N.A.: Exact solutions of the generalized Kuramoto–Sivashinsky equation. Phys. Lett. A 147, 287–291 (1990)
Kudryashov, N.A.: On types of nonlinear nonintegrable equations with exact solutions. Phys. Lett. A 155, 269–275 (1991)
Ma, W.X., Huang, T.W., Zhang, Y.: A multiple exp-function method for nonlinear differential equations and its application. Phys. Scr. 82, 065003 (2010)
Ma, W.X., Lee, J.H.: A transformed rational function method and exact solutions to the (3 + 1)-dimensional Jimbo–Miwa equation. Chaos Solitons Fractals 42, 1356–1363 (2009)
Bekir, A., Unsal, O.: Analytic treatment of nonlinear evolution equations using first integral method. Pramana J. Phys. 79, 3–17 (2012)
Tascan, F., Bekir, A., Koparan, M.: Travelling wave solutions of nonlinear evolutions by using the first integral method. Commun. Nonlin. Sci. Numer. Simul. 14, 1810–1815 (2009)
Zhou, Q., Zhu, Q., Yu, H., Liu, Y., Wei, C., Yao, P., Bhrawy, A.H., Biswas, A.: Bright, dark and singular optical solitons in a cascaded system. Laser Phys. 25(2), 025402 (2015)
Xu, Y., Zhou, Q., Bhrawy, A.H., Khan, K.R., Mahmood, M.F., Biswas, A., Belic, M.: Bright soliton in optical metamaterials by traveling wave hypothesis. Optoelectron. Adv. Mater. Rapid Commun. 9(3–4), 384–387 (2015)
Savescu, M., Alshaery, A.A., Hilal, E.M., Bhrawy, A.H., Zhou, Q., Biswas, A.: Optical solitons in DWDM system with four-wave mixing. Optoelectron. Adv. Mater. Rapid Commun. 9(1–2), 14–19 (2015)
Savescu, M., Bhrawy, A.H., Hilal, E.M., Alshaery, A.A., Moraru, L., Biswas, A.: Optical solitons in birefringent fibers with fourwave mixing for parabolic law nonlinearity. Optoelectron. Adv. Mater. Rapid Commun. 9(1–2), 10–13 (2015)
Zhou, Q., Zhu, Q., Bhrawy, A.H., Biswas, A.: Combined optical solitons with nonlinear dispersion and spatio-temporal dispersion. Optoelectron. Adv. Mater. Rapid Commun. 9(1–2), 1–4 (2015)
Vega-Guzman, J., Zhou, Q., Alshaery, A.A., Hilal, E.M., Bhrawy, A.H., Biswas, A.: Optical solitons in cascaded system with spatio-temporal dispersion by ansatz approach. J. Optoelectron. Adv. Mater. 17(1–2), 165–171 (2015)
Guzman, J.-V., Zhou, Q., Alshaery, A.A., Hilal, E.M., Bhrawy, A.H., Biswas, A.: Optical solitons in cascaded system with spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 17(1–2), 74–81 (2015)
Zhou, Q., Zhu, Q., Savescu, M., Bhrawy, A., Biswas, A.: Optical solitons with nonlinear dispersion in parabolic law medium. Proc. Rom. Acad. Ser. A 16(2), 152–159 (2015)
Savescu, M., Bhrawy, A.H., Hilal, E.M., Alshaery, A.A., Biswas, A.: Optical solitons in Magneto-optic waveguides with spatio-temporal dispersion. Frequenz 68(9–10), 445–451 (2014)
Topkara, E., Milovic, D., Sarma, A.K., Majid, F., Biswas, A.: A study of optical solitons with kerr and power law nonlinearities by He’s variational principle. J. Eur. Opt. Soc. 4, 09050 (2009)
Topkara, E., Milovic, D., Sarma, A.K., Zerrad, E., Biswas, A.: Optical soliton perturbation with full nonlinearity in non-Kerr law media. J. Opt. Fiber Commun. Res. 7(1–4), 43–59 (2010)
Biswas, A., Topkara, E., Johnson, S., Zerrad, E., Konar, S.: Quasi-stationary optical solitons in non-kerr law media with full nonlinearity. J. Nonlin. Opt. Phys. Mater. 20(3), 309–325 (2011)
Eslami, M., Mirzazadeh, M.: Topological 1-soliton solution of nonlinear Schrödinger equation with dual-power law nonlinearity in nonlinear optical fibers. Eur. Phys. J. Plus 128(11), 1–7 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Eslami, M., Mirzazadeh, M. Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn 83, 731–738 (2016). https://doi.org/10.1007/s11071-015-2361-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-015-2361-1