Skip to main content
SpringerLink
Log in

Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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)

    Article  MathSciNet  MATH  Google Scholar 

  2. 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)

    Article  MathSciNet  MATH  Google Scholar 

  3. Majid, F.: 1-Soliton solution of the Biswas–Milovic equation with log law nonlinearity. Casp. J. Math. Sci. 1(2), 88–93 (2012)

    Google Scholar 

  4. 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)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kohl, R., Tinaztepe, R., Chowdhury, A.: Soliton perturbation theory of Biswas–Milovic equation. Optik 125(8), 1926–1936 (2014)

    Article  Google Scholar 

  6. 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)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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)

    Google Scholar 

  8. Manafian, J., Lakestani, M.: Optical solitons with Biswas–Milovic equation for Kerr law nonlinearity. Eur. Phys. J. Plus 130(61), 1–12 (2015)

    Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. 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)

    Article  MathSciNet  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Google Scholar 

  15. 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)

    Article  MathSciNet  Google Scholar 

  16. Zhou, Q., Liu, S.: Dark optical solitons in quadratic nonlinear media with spatio-temporal dispersion. Nonlin. Dyn. 81(1–2), 733–738 (2015)

    Article  MathSciNet  Google Scholar 

  17. 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)

    Article  Google Scholar 

  18. 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)

    Article  MathSciNet  Google Scholar 

  19. Biswas, A., Konar, S.: Introduction to Non-Kerr Law Optical Solitons. CRC Press, Boca Raton (2007)

    MATH  Google Scholar 

  20. Biswas, A.: Quasi-stationary non-Kerr law optical solitons. Opt. Fiber Technol. 9(4), 224–259 (2003)

    Article  Google Scholar 

  21. Antonova, M., Biswas, A.: Adiabatic parameter dynamics of perturbed solitary waves. Commun. Nonlin. Sci. Numer. Simul. 14(3), 734–748 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. 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)

    Article  MathSciNet  MATH  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. 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)

    Article  MATH  Google Scholar 

  25. Biswas, A.: Perturbation of solitons with non-Kerr law nonlinearity. Chaos Solitons Fractals 13(4), 815–823 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. 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)

    Article  MATH  Google Scholar 

  27. Wazwaz, A.M.: The sine–cosine method for obtaining solutions with compact and noncompact structures. Appl. Math. Comput. 159(2), 559–576 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wazwaz, A.M.: A sine–cosine method for handling nonlinear wave equations. Math. Comput. Model. 40(5–6), 499–508 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  29. 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)

    Article  Google Scholar 

  30. 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)

    Article  MathSciNet  Google Scholar 

  31. 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)

    Article  MathSciNet  MATH  Google Scholar 

  32. 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)

    Article  MathSciNet  MATH  Google Scholar 

  33. Kudryashov, N.A.: Exact soliton solutions of the generalized evolution equation of wave dynamics. J. Appl. Math. Mech. 52, 361–365 (1988)

    Article  MathSciNet  Google Scholar 

  34. Kudryashov, N.A.: On one of methods for finding exact solutions of nonlinear differential equations. Commun. Nonlin. Sci. Numer. Simul. 17, 2248–2256 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  35. Kudryashov, N.A.: Exact solutions of the generalized Kuramoto–Sivashinsky equation. Phys. Lett. A 147, 287–291 (1990)

    Article  MathSciNet  Google Scholar 

  36. Kudryashov, N.A.: On types of nonlinear nonintegrable equations with exact solutions. Phys. Lett. A 155, 269–275 (1991)

    Article  MathSciNet  Google Scholar 

  37. 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)

    Article  MATH  Google Scholar 

  38. 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)

    Article  MathSciNet  MATH  Google Scholar 

  39. Bekir, A., Unsal, O.: Analytic treatment of nonlinear evolution equations using first integral method. Pramana J. Phys. 79, 3–17 (2012)

    Article  MATH  Google Scholar 

  40. 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)

    Article  Google Scholar 

  41. 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)

    Article  Google Scholar 

  42. 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)

    Google Scholar 

  43. 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)

    Google Scholar 

  44. 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)

  45. 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)

    Google Scholar 

  46. 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)

    Google Scholar 

  47. 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)

    Google Scholar 

  48. 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)

    MathSciNet  Google Scholar 

  49. 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)

    Google Scholar 

  50. 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)

    Article  Google Scholar 

  51. 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)

    Article  MATH  Google Scholar 

  52. 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)

    Article  Google Scholar 

  53. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    M. Eslami

  2. Department of Engineering sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, 44891-63157, Iran

    M. Mirzazadeh

Authors
  1. M. Eslami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Mirzazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Mirzazadeh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2361-1

Keywords

Search

Navigation