Skip to main content
Log in

Optical solitons with Biswas–Milovic equation by extended trial equation method

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

Abstract

This paper addresses the Biswas–Milovic equation as a generalized model for soliton propagation through optical wave guides. The extended trail equation method reveals several forms of soliton solution such as bright, dark and singular solitons. Other wave solutions fall out as by-product of this integration algorithm.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Biswas, A., Milovic, D.: Bright and dark solitons of the generalized nonlinear schrödinger’s equation. Commun. Nonlinear Sci. Numer. Simulat. 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. Nonlinear Sci. Numer. Simulat. 15(9), 2320–2330 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Eslami, M., Mirzazadeh, M.: Optical solitons with Biswas–Milovic equation for power law and dual-power law nonlinearities. Nonlinear Dyn. 83(1), 731–738 (2016)

    Article  MathSciNet  Google Scholar 

  4. Zhou, Q.: Optical solitons for Biswas-Milovic model with Kerr law and parabolic law nonlinearities. Nonlinear Dyn. doi:10.1007/s11071-015-2516-0

  5. 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 

  6. Sturdevant, B.: Topological 1-soliton solution of the Biswas–Milovic equation with power law nonlinearity. Nonlinear Anal. Real World Appl. 11(4), 2871–2874 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. 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 

  9. Mirzazadeh, M., Eslami, M., Hassan Arnous, A.: Dark optical solitons of Biswas-Milovic equation with dual-power law nonlinearity. Eur. Phys. J. Plus. 130(4), 1–7 (2015)

    Google Scholar 

  10. 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 

  11. 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 

  12. 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 

  13. Zhou, Q., Yao, D., Chen, F.: Analytical study of optical solitons in media with Kerr and parabolic-law nonlinearities. J. Modern Opt. 60(19), 1652–1657 (2013)

    Article  MathSciNet  Google Scholar 

  14. 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 

  15. 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 

  16. Safdar, A., Rizvi, S.T.R., Younis, M.: Traveling wave solutions for nonlinear dispersive water-wave systems with time-dependent coefficients. Nonlinear Dyn. 3(1), 77–79 (2014)

    Google Scholar 

  17. Younis, M., Ali, S., Mahmood, S.A.: Solitons for compound KdV-Burgers equation with variable coefficients and power law nonlinearity. Nonlinear Dyn. 81(3), 1191–1196 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. 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. Nonlinear Dyn. 80(3), 1365–1371 (2015)

    Article  Google Scholar 

  20. Zhou, Q., Zhu, Q., Yu, H., Xiong, X.: Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion. Nonlinear Dyn. 80(1–2), 983–987 (2015)

    Article  MathSciNet  Google Scholar 

  21. 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 

  22. Vega-Guzman, J., Alshaery, A.A., Hilal, E.M., Bhrawy, A.H., Mahmood, M.F., Moraru, L., Biswas, A.: Optical soliton perturbation in magneto-optic waveguides with spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 16(9–10), 1063–1070 (2014)

    Google Scholar 

  23. Savescu, M., Hilal, E.M., Alshaery, A.A., Bhrawy, A.H., Moraru, L., Biswas, A.: Optical solitons with quadratic nonlinearity and spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 16(5–6), 619–623 (2014)

    Google Scholar 

  24. Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Manrakhan, W., Savescu, M., Biswas, A.: Dispersive optical solitons with Schrodinger-Hirota equation. J. Nonlinear Opt. Phys. Mater. 23(1), 1450014 (2014)

    Article  Google Scholar 

  25. Savescu, M., Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Khan, K.R., Mahmood, M.F., Biswas, A.: Optical solitons in nonlinear directional couplers with and spatio-temporal dispersion. J. Modern Opt. 61(5), 442–459 (2014)

    Article  MathSciNet  Google Scholar 

  26. Savescu, M., Bhrawy, A.H., Hilal, E.M., Alshaery, A.A., Biswas, A.: Opical solitons in Birefringent fibers with four-wave mixing for kerr law nonlinearity. Rom. J. Phys. 59(5–6), 582–589 (2014)

    Google Scholar 

  27. Bhrawy, A.H., Alshaary, A.A., Hilal, E.M., Milovic, D., Moraru, L., Savescu, M., Biswas, A.: Opical solitons with polynomial and triple power law nonlinearities and with spatio-temporal dispersion. Proc. Rom. Acad. Series A. 15(3), 235–240 (2014)

    Google Scholar 

  28. Alshaery, A.A., Bhrawy, A.H., Hilal, E.M., Biswas, A.: Bright and singular solitons in Quadratic nonlinear media. J. Electromagn. Waves Appl. 28(3), 275–280 (2014)

    Article  MathSciNet  Google Scholar 

  29. Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Jovanoski, Z., Biswas, A.: Bright and singular solitons in a Cascaded system. Optik 125(20), 6162–6165 (2014)

    Article  Google Scholar 

  30. Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Khan, K.R., Mahmood, M.F., Biswas, A.: Opical soliton perturbation with spatio-temporal dispersion in parabolic and dual-power law media by semi-inverse variational principle. Optik 125(17), 4945–4950 (2014)

    Article  Google Scholar 

  31. Biswas, A., Bhrawy, A.H., Alshaery, A.A., Hilal, E.M.: Thirring optical soliton with kerr law nonlinearity. Optik 125(17), 4946–4948 (2014)

    Google Scholar 

  32. Biswas A, A., Konar, S.: Introduction to non-Kerr law optical solitons. CRC Press, Boca Raton (2007)

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  35. 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 

  36. 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 

  37. Biswas, A.: Topological 1-soliton solution of the nonlinear Schrödinger’s equation with Kerr law nonlinearity in 1+ 2 dimensions. Commun. Nonlinear Sci. Numer. Simulat. 14(7), 2845–2847 (2009)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  39. Kohl, R., Milovic, D., Zerrad, E., Biswas, A.: Soliton perturbation theory for dispersion-managed optical fibers. J. Nonlinear Opt. Phys. Mater. 18(2), 227–270 (2009)

    Article  MATH  Google Scholar 

  40. Biswas, A.: Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients. Nonlinear Dyn. 58(1–2), 345–348 (2009)

  41. Sassaman, R., Biswas, A.: Topological and non-topological solitons of the Klein-Gordon equations in 1+ 2 dimensions. Nonlinear Dyn. 61(1–2), 23–28 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  42. Krishnan, E.V., Triki, H., Labidi, M., Biswas, A.: A study of shallow water waves with Gardner’s equation. Nonlinear Dyn. 66(4), 497–507 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. Wang, G.W., Xu, T.Z., Ebadi, G., Johnson, S., Strong, A.J., Biswas, A.: Singular solitons, shock waves, and other solutions to potential KdV equation. Nonlinear Dyn. 76(2), 1059–1068 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  44. Razborova, P., Kara, A.H., Biswas, A.: Additional conservation laws for Rosenau-KdV-RLW equation with power law nonlinearity by Lie symmetry. Nonlinear Dyn. 79(1), 743–748 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  45. Biswas, A., Kara, A.H., Bokhari, A.H., Zaman, F.D.: Solitons and conservation laws of Klein-Gordon equation with power law and log law nonlinearities. Nonlinear Dyn. 73(4), 2191–2196 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  46. Biswas, A.: Solitary waves for power-law regularized long-wave equation and R (m, n) equation. Nonlinear Dyn. 59(3), 423–426 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  47. Liu, C.-S.: Travelling wave solutions of triple sine-gordon equation. Chin. Phys. Lett. 21(12), 2369 (2004)

    Article  Google Scholar 

  48. Liu, C.-S.: All single traveling wave solutions to (3+ 1)-dimensional nizhnok novikov veselov equation. Commun. Theor. Phys. 45, 991–992 (2006)

    Article  MathSciNet  Google Scholar 

  49. Liu, C.-S.: Exact traveling wave solutions for a kind of generalized Ginzburg-Landau equation. Commun. Theor. Phys. 43(5), 787 (2005)

    Article  MathSciNet  Google Scholar 

  50. Liu, C.-S.: Classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation. Commun. Theor. Phys. 48(4), 601 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  51. Liu, C.-S.: Representations and classification of traveling wave solutions to sinh-Gordon equation. Commun. Theor. Phys. 49(1), 153 (2008)

    Article  MathSciNet  Google Scholar 

  52. Liu, C.-S.: Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Comput. Phys. Commun. 181(2), 317–324 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  53. Filiz, A., Sonmezoglu, A., Ekici, M., Duran, D.: A new approach for soliton solutions of RLW equation and (1+2)-dimensional nonlinear Schrödinger’s equation. Math. Rep. 17(67), 43–56 (2015)

    MathSciNet  Google Scholar 

  54. Ekici, M., Mirzazadeh, M., Eslami, M.: Solitons and other solutions to Boussinesq equation with power law nonlinearity and dual dispersion. Nonlinear Dyn. doi:10.1007/s11071-015-2515-1

  55. Pandir, Y., Gurefe, Y., Kadak, U., Misirli, E.: Classification of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstract and Applied Analysis. 2012 (2012). Article ID 478531, 16 pages

Download references

Acknowledgments

The work was supported by the National Natural Science Foundation of China under the grant number 11547149.

Author information

Authors and Affiliations

Authors

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

Zhou, Q., Ekici, M., Sonmezoglu, A. et al. Optical solitons with Biswas–Milovic equation by extended trial equation method. Nonlinear Dyn 84, 1883–1900 (2016). https://doi.org/10.1007/s11071-016-2613-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-2613-8

Keywords

Navigation