An efficient method to compute solitary wave solutions of fractional Korteweg–de Vries equations

ABSTRACT

Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg–de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation techniques of acceleration. This combination improves the performance in both the velocity of convergence and the computation of profiles for limiting values of the fractional parameter. The algorithm is described and numerical experiments of validation are presented. The accuracy attained by the procedure can be used to investigate additional properties of the waves. This approach is illustrated here by analysing the speed–amplitude relation.

KEYWORDS:

• Fractional KdV equations
• solitary waves
• Petviashvili method
• acceleration techniques

2010 AMS SUBJECT Classification:

• 65H10
• 65M70
• 65Z05

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by Ministerio de Economía y Competitividad under the Research [grant number MTM2014-54710-P].