Skip to main content
Log in

Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach

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

Abstract

In this paper, the resonant nonlinear Schrödinger’s equation is studied with four forms of nonlinearity and time-dependent coefficients. The trial solution method is employed to solve the governing equations. Solitons and singular periodic solutions are obtained. The constraint conditions naturally emerge from the solution structure that are needed for its existence.

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.: Soliton solutions of the perturbed resonant nonlinear dispersive Schrödinger’s equation with full nonlinearity by semi-inverse variational principle. Quantum Phys. Lett. 1(2), 79–84 (2012)

    Google Scholar 

  2. Bulut, H., Pandir, Y., Demiray, S.T.: Exact solutions of nonlinear Schrödinger’s equation with dual power-law nonlinearity by extended trial equation method. Waves Random Complex Media 24(4), 439–451 (2014)

    Article  MathSciNet  Google Scholar 

  3. Eslami, M., Mirzazadeh, M., Biswas, A.: Soliton solutions of the resonant nonlinear Schrödinger’s equation in optical fibers with time dependent coefficients by simplest equation approach. J. Mod. Optics. 60(19), 1627–1636 (2013)

    Article  Google Scholar 

  4. Eslami, M., Mirzazadeh, M., Vajargah, B.F., Biswas, A.: Optical solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients by the first integral method. Optik 125(9), 3107–3116 (2014)

    Article  Google Scholar 

  5. Geng, X., Lv, Y.: Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation. Nonlinear Dyn. 69(4), 1621–1630 (2012)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Gupta, R.K., Kumar, V., Jiwari, R.: Exact and numerical solutions of coupled short pulse equation with time-dependent coefficients. Nonlinear Dyn. 79(1), 455–464 (2015)

    Article  MathSciNet  Google Scholar 

  8. Gurefe, Y., Sonmezoglu, A., Misirli, E.: Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics. Pramana 77, 1023–1029 (2011)

    Article  Google Scholar 

  9. Krishnan, E.V., Kumar, S., Biswas, A.: Solitons and other nonlinear waves of Boussinesq equation. Nonlinear Dyn. 70(2), 1213–1221 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. Liu, C.S.: Trial equation method to nonlinear evolution equations with rank inhomogeneous: mathematical discussions and its applications. Commun. Theor. Phys. 45, 219–223 (2006)

    Article  Google Scholar 

  11. Mirzazadeh, M., Eslami, M., Milovic, D., Biswas, A.: Topological solitons of resonant nonlinear Schrödinger’s equation with dual-power law nonlinearity using \(G^{\prime }/G\)-expansion technique. Optik 125(19), 5480–5489 (2014)

    Article  Google Scholar 

  12. Mirzazadeh, M., Eslami, M., Vajargah, B.F., Biswas, A.: Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger’s equation with power law nonlinearity. Optik 125(9), 4246–4256 (2014)

    Article  Google Scholar 

  13. Rui, C., Jian, Z.: Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient. Chin. Phys. B 22(10), 100507 (2013)

    Article  Google Scholar 

  14. Triki, H., Hayat, T., Aldossary, O.M., Biswas, A.: Bright and dark solitons for the resonant nonlinear Schrödinger’s equation with time- dependent coefficients. Opt. Laser Technol. 44, 2223–2231 (2012)

    Article  Google Scholar 

  15. Triki, H., Yildirim, A., Hayat, T., Aldossary, O.M., Biswas, A.: 1-soliton solution of the generalized resonant nonlinear dispersive Schrödinger’s equation with time-dependent coefficients. Adv. Sci. Lett. 16, 309–312 (2012)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anjan Biswas.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mirzazadeh, M., Arnous, A.H., Mahmood, M.F. et al. Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach. Nonlinear Dyn 81, 277–282 (2015). https://doi.org/10.1007/s11071-015-1989-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-1989-1

Keywords

Navigation