Modelling solitary waves of a fifth-order non-linear wave equation

Abstract

A numerical solution of a fifth-order non-linear dispersive wave equation is set up using collocation of seventh-order B-spline interpolation functions over finite elements. A linear stability analysis shows that this numerical scheme, based on a Crank–Nicolson approximation in time, is unconditionally stable. The method is used to model the behaviour of solitary waves.

Keywords:

• Finite element methods
• Collocation splines
• Solitons
• Solitons waves

Acknowledgements

Turabi Geyikli gratefully acknowledges the financial support given by the İnönü U¨niversity Research Fund (Turkey) under contracts İU¨AF-2003/73.