Skip to main content
Log in

Soliton Solution of Some Nonlinear PDEs and Its Applications

  • Full length article
  • Published:
International Journal of Applied and Computational Mathematics Aims and scope Submit manuscript

Abstract

The variable coefficient \(3+1\) dimensional coupled Nonlinear Schrödinger (NLS) equation is investigated, the equation is transformed into a form of bilinear expressions by the bilinear method, the single and double soliton solutions of the equation are obtained by using symbolic computation. The Backlund transformation (BTs) in the bilinear form using the bilinear exchange formular was also deduced.

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

Data Availability

Enquiries about data availability should be directed to the authors.

References

  1. Asghar, A., Aly, R.S., Lu, D.: New solitary wave solutions of some nonlinear models and their applications. Adv. Differ. Equ. 1–12 (2018)

  2. Ting-Ting, J., Yu-Zhen, C., Hui-Qin, H.: Multi-soliton solutions and Breathers for the generalized coupled nonlinear Hirota equations via the Hirota method. Superlatt. Microstruct. 105, 172–182 (2017)

    Article  Google Scholar 

  3. Jafarian, A., Ghaderi, P., Golmankhaneh, A.K.: Construction of soliton solution to the Kadomtsev–Petviashvili-II equation using homotopy analysis method. Rom. Rep. Phys. 65, 76–83 (2013)

    Google Scholar 

  4. Gilson, C., Lambert, F., Nimmo, J., Willox, R.: On the combinatorics of the Hirota D-operators. Proc. R. Soc. Lond. A. 452, 223–234 (1996)

    Article  MathSciNet  Google Scholar 

  5. Lambert, F., Loris, I., Springael, J.: Classical Darboux transformations and the KP hierarchy. Inverse Probl. 17, 1067–1074 (2001)

    Article  MathSciNet  Google Scholar 

  6. Lambert, F., Springael, J.: Soliton equations and simple combinatorics. Acta Appl. Math. 102, 147–178 (2008)

    Article  MathSciNet  Google Scholar 

  7. Fan, E.G.: The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials. Phys. Lett. A. 375, 493–497 (2011)

    Article  MathSciNet  Google Scholar 

  8. Zakharov, V.E., Shabat, A.B.: An exact theory of two-dimensional self-focussing and of one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP. 34, 62–69 (1972)

    Google Scholar 

  9. Chen, Y.X., Jiang, Y.B.: Spatiotemporal soliton structures in \((3+1)-\)dimensional \(PT-\) symmetric nonlinear couplers with gain and loss. Nonlinear Dyn. 82, 2015–2057 (2015)

    MathSciNet  Google Scholar 

  10. 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  Google Scholar 

  11. Bhrawy, A.H., Zaky, M.A., Baleanu, D.: New numerical approximations for space-time fractional burgers’ equations via a Legendre spectral-collocation method. Rom. Rep. Phys. 67, 340–349 (2015)

    Google Scholar 

  12. Zhou, G.P., Dai, C.Q., Chen, Y.X.: Nonlinear tummelling of superposed Akhmediev breather in PT - symmetric inhomogeneous nonlinear couplers with gain and loss. Opt. Commun. 345, 31–36 (2015)

    Article  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saviour Worlanyo Akuamoah.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akuamoah, S.W., Ayimah, J.C., Mahama, F. et al. Soliton Solution of Some Nonlinear PDEs and Its Applications. Int. J. Appl. Comput. Math 8, 69 (2022). https://doi.org/10.1007/s40819-022-01276-7

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40819-022-01276-7

Keywords

Navigation