Skip to main content
SpringerLink
Log in

Invariant solutions of Biswas-Milovic equation

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

Abstract

The Biswas-Milovic equation in generalized form and with power law nonlinearity is analyzed for Lie symmetries. The classical Lie group method is applied to derive symmetries of this equation, and the ordinary differential equations deduced are further studied; and some exact solutions are obtained.

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., Khalique, C.: Stationary solitons for nonlinear dispersive Schrödinger’s equation. Nonlinear Dyn. 63(4), 623–626 (2011)

    Article  MathSciNet  Google Scholar 

  2. Biswas, A., Milovic, D.: Bright and dark solitons of the generalized nonlinear Schrödinger’s equation. Commun. Nonlinear Sci. Numer. Simul. 15, 1473–1484 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Biswas, A., Mirzazadeh, M., Eslami, M., Milovic, D., Belic, M.: Solitons in optical metamaterials by functional variable method and first integral approach. Frequenz 68, 525–530 (2014)

    Article  Google Scholar 

  4. Bluman, G., Cole, J.: The general similarity of the heat equation. J. Math. Mech. 18(11), 1025–1042 (1969)

    MathSciNet  MATH  Google Scholar 

  5. Bluman, G., Cole, J.: Similarity Methods for Differential Equations, vol. 13. Springer, New York (1974)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Gupta, R., Bansal, A.: Similarity reductions and exact solutions of generalized Bretherton equation with time-dependent coefficients. Nonlinear Dyn. 71(1–2), 1–12 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Khalique, C., Biswas, A.: A Lie symmetry approach to nonlinear Schrödinger’s equation with non-kerr law nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 14(12), 4033–4040 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kumar, S.: Painlevé analysis and invariant solutions of Vakhnenko-Parkes (VP) equation with power law nonlinearity. Nonlinear Dyn. 85(2), 1275–1279 (2016)

  10. Lü, X., Zhu, H., Yao, Z., Meng, X., Zhang, C., Zhang, C., Tian, B.: Multi-soliton solutions in terms of double Wronskian determinant for a generalized variable-coefficient nonlinear Shrödinger’s equation from plasma physics, arterial mechanics, fluid dynamics and optical communications. Annal Phys. 323(8), 1947–1955 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mirzazadeh, M., Ekici, M., Sonmezoglu, A., Eslami, M., Zhou, Q., Kara, A.H., Milovic, D., Majid, F.B., Biswas, A., Belic, M.: Optical solitons with complex Ginzburg-Landau equation. Nonlinear Dyn. 85, 1979–2016 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mirzazadeh, M., Eslami, M., Zerrad, E., Mahmood, M., 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)

    Article  MathSciNet  MATH  Google Scholar 

  13. Olver, P.: Applications of Lie Groups to Differential Equations, vol. 107. Springer, New York (1986)

    MATH  Google Scholar 

  14. Zhou, Q.: Optical solitons in the parabolic law media with high-order dispersion. Optik-Int. J. Light Electron Opt. 125, 5432–5435 (2014)

    Article  Google Scholar 

  15. Zhou, Q.: Optical solitons for Biswas-Milovic model with Kerr law and parabolic law nonlinearities. Nonlinear Dyn. 84, 677–681 (2016)

    Article  MathSciNet  Google Scholar 

  16. Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M.: Optical solitons with Biswas-Milovic equation by extended G’/G-expansion method. Optik-Int. J. Light Electron Opt. 127, 6277–6290 (2016)

    Article  MATH  Google Scholar 

  17. Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Analytical study of solitons to Biswas–Milovic model in nonlinear optics. J. Modern Opt. (2016). doi:10.1080/09500340.2016.1184719

  18. Zhou, Q., Ekici, M., Sonmezoglu, A., Mirzazadeh, M., Eslami, M.: Optical solitons with Biswas-Milovic equation by extended trial equation method. Nonlinear Dyn. 84, 1883–1900 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubicquintic nonlinearity and third-order dispersion. Nonlinear Dyn. 80, 1365–1371 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Zhou, Q., Mirzazadeh, M., Ekici, M., Sonmezoglu, A.: Analytical study of solitons in non-kerr nonlinear negative-index materials. Nonlinear Dyn. 86, 623–638 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhou, Q., Mirzazadeh, M., Zerrad, E., Biswas, A., Belic, M.: Bright, dark, and singular solitons in optical fibers with spatio-temporal dispersion and spatially dependent coefficients. J. Modern Opt. 63(10), 950–954 (2016)

    Article  Google Scholar 

  23. Zhou, Q., Zhu, Q.: Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion. J. Modern Opt. 62(6), 483–486 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This research is funded by UGC Start-Up Grant and seed money Grant of Central University of Punjab, Bathinda. The author thankfully acknowledge this support from UGC and Central University of Punjab, Bathinda.

Author information

Authors and Affiliations

  1. Centre for Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab, 151001, India

    Sachin Kumar

Authors
  1. Sachin Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sachin Kumar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kumar, S. Invariant solutions of Biswas-Milovic equation. Nonlinear Dyn 87, 1153–1157 (2017). https://doi.org/10.1007/s11071-016-3105-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-016-3105-6

Keywords

Search

Navigation