Skip to main content

Exact Solutions for \((2+1)\)–Dimensional Nonlinear Schrödinger Schrodinger Equation Based on Modified Extended tanh Method

  • Conference paper
  • First Online:
Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1074))

Abstract

A modified extended tanh method is used to construct more general exactsolutions of a (2+1)-dimensional nonlinear Schrödinger equation by traveling wave map, and the partial differential is changed into complex algebraic equations. With the aid of Maple and Matlab software, we obtain some exact explicit solutions, such as kink wave solutions, peakon wave solutions, periodic wave solutions and their images.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Gray, P., Scott, S.: Chemical Oscillations and Instabilities. Clarendon Press, Oxford (1990)

    Google Scholar 

  2. Murray, J.: Mathematical Biology. Springer, Berlin (1989)

    Book  Google Scholar 

  3. Dingjiang, H., Desheng, L., Hongqing, Z.: Explicit and exact travelling wave solutions for the generalized derivative Schrödinger equation. Chaos, Solitons Fractals 31, 586–593 (2007)

    Article  MathSciNet  Google Scholar 

  4. Vakhnenko, V.O., Parkes, E.J., Morrison, A.J.: A Bäcklund transformation and the inverse scattering transform method for the generalized Vakhnenko equation. Chaos, Solitons Fractals 17(4), 683–692 (2003)

    Article  MathSciNet  Google Scholar 

  5. Yomba, E.: The extended Fans sub-equation method and its application to KDV-mKDV BKK and variant Boussinesq equation. Phys. Lett. A336, 463–476 (2005)

    Article  MathSciNet  Google Scholar 

  6. Matveev, V.A., Salle, M.A.: Darboux Transformation and Solitons. Springer, Berlin (2001)

    MATH  Google Scholar 

  7. Khuri, S.A.: A complex tanh-function method applied to nonlinear equations of Schrödinger type. Chaos, Solitons Fractals 20, 1037–1040 (2004)

    Article  MathSciNet  Google Scholar 

  8. Kavitha, L., Akila, N., Prabhu, A., Kuzmanovska-Barandovska, O., Gopi, D.: Exact solitary solutions of an inhomogeneneous modified nonlinear Schrödinger equation with competing nonlinearities. Math. Comput. Modell. 53, 1095–1110 (2011)

    Article  Google Scholar 

  9. Fan, E., Hon, Y.C.: Applications of extended tanh method to special types of nonlinear equations. Appl. Math. Comput. 141, 351–358 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Malfliet, W.: Solitary wave solutions of nonlinear wave equations. Amer. J. Phys. 60(7), 650–654 (1992)

    Article  MathSciNet  Google Scholar 

  11. Malfliet, W.: The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 164–165, 529–541 (2004)

    Article  MathSciNet  Google Scholar 

  12. Wazwaz, A.-M.: The Camassa-Holm-KP equations with compact and noncompact travelling wave solutions. Appl. Math. Comput. 170, 347–360 (2005)

    MathSciNet  MATH  Google Scholar 

  13. Wazwaz, A.-M.: The tanh and the sine-cosine methods for the complex modified KdV and the generalized KdV equations. Comput. Math. Appl. 49, 1101–1112 (2005)

    Article  MathSciNet  Google Scholar 

  14. Wazwaz, A.-M.: The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Appl. Math. Comput. 187, 1131–1142 (2007)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledges the support of the Yunnan Tobacco Company’s science and technology project “Research on Data Resource Mining Based on Multi-objective Decision Making”.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Longwei Chen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Xiong, M., Chen, L., Li, C., Wang, J. (2020). Exact Solutions for \((2+1)\)–Dimensional Nonlinear Schrödinger Schrodinger Equation Based on Modified Extended tanh Method. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_24

Download citation

Publish with us

Policies and ethics