Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation

Authors:
P. Saucez;A. Vande Wouwer;P. A. Zegeling
Affiliations:
Service de Mathématique et Recherche Opérationnelle, Faculté Polytechnique de Mons, Belgium;Service d'Automatique, Faculté Polytechnique de Mons, Mons, Belgium;Mathematical Institute, Utrecht University, The Netherlands
Venue:
Journal of Computational and Applied Mathematics - Special issue on the method of lines: Dedicated to Keith Miller
Year:
2005

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Abstract

In this paper, we investigate the dynamics and interaction properties of recently discovered "embedded solitons" in an extended fifth-order KdV model inspired by water waves in the presence of surface tension. The dynamical behaviour of the solitons can be efficiently followed by using a moving or an adaptive finite difference mesh in combination with a suitable time-integrator. We will demonstrate this numerically for different types of wave solutions, such as solitary waves, multihumped waves, and interacting waves.