A self-adjusting algorithm for solitary wave simulations

Abstract

We introduce a practical algorithm to automate the simulations of solitary wave solutions of some nonlinear dispersive wave equations. The full discretization consists of a spatial discretization with a local basis and an invariant preserving time integrator. The algorithm includes a dynamic cleaning of dispersive tails and an automatic detection of the complete separation of the main pulses.

Keywords:

• solitary waves
• cleaning procedures
• conservative methods

2010 AMS Subject Classifications:

• 65M20
• 65M99
• 35Q53
• 76B25

Acknowledgements

This research has been supported by MCINN project MTM2011-23417 cofinanced by FEDER funds. The authors are very grateful to Prof. Ángel Durán for several valuable suggestions.