Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation
Publication date
2005-11-15
Authors
Saucez, P.
Vande Wouwer, Alain
Zegeling, Paul Andries
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Document Type
Article
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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.
Keywords
Adaptive mesh method, Finite differences, Method of lines, Nonlinear dynamics, Solitary waves, Water waves, Wave interaction, Computational Mathematics, Applied Mathematics
Citation
Saucez, P, Vande Wouwer, A & Zegeling, P A 2005, 'Adaptive method of lines solutions for the extended fifth-order Korteweg-de Vries equation', Journal of Computational and Applied Mathematics, vol. 183, no. 2, pp. 343-357. https://doi.org/10.1016/j.cam.2004.12.028