233
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

A conservative exponential time differencing method for the nonlinear cubic Schrödinger equation

&
Pages 230-251 | Received 05 May 2015, Accepted 15 Sep 2015, Published online: 29 Oct 2015
 

ABSTRACT

A mass and energy conservative exponential time differencing scheme using the method of lines is proposed for the numerical solution of a certain family of first-order time-dependent PDEs. The resulting nonlinear system is solved with an unconditionally stable modified predictor–corrector method using a second-order explicit scheme. The efficiency of the method introduced is analyzed and discussed by applying it to the nonlinear cubic Schrödinger equation. The results arising from the experiments for the single, the double soliton waves and the system of two Schrödinger equations are compared with relevant known ones.

AMS SUBJECT CLASSIFICATIONS:

Acknowledgements

The authors are grateful to the referees for their constructive comments and suggestions, which have helped to improve the quality and presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.