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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Gray, P., Scott, S.: Chemical Oscillations and Instabilities. Clarendon Press, Oxford (1990)
Murray, J.: Mathematical Biology. Springer, Berlin (1989)
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)
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)
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)
Matveev, V.A., Salle, M.A.: Darboux Transformation and Solitons. Springer, Berlin (2001)
Khuri, S.A.: A complex tanh-function method applied to nonlinear equations of Schrödinger type. Chaos, Solitons Fractals 20, 1037–1040 (2004)
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)
Fan, E., Hon, Y.C.: Applications of extended tanh method to special types of nonlinear equations. Appl. Math. Comput. 141, 351–358 (2003)
Malfliet, W.: Solitary wave solutions of nonlinear wave equations. Amer. J. Phys. 60(7), 650–654 (1992)
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)
Wazwaz, A.-M.: The Camassa-Holm-KP equations with compact and noncompact travelling wave solutions. Appl. Math. Comput. 170, 347–360 (2005)
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)
Wazwaz, A.-M.: The extended tanh method for abundant solitary wave solutions of nonlinear wave equations. Appl. Math. Comput. 187, 1131–1142 (2007)
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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
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
DOI: https://doi.org/10.1007/978-3-030-32456-8_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32455-1
Online ISBN: 978-3-030-32456-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)