Behaviour of the extended Toda lattice

Wattis, Jonathan A.D.; Gordoa, Pilar R.; Pickering, Andrew

Abstract

We consider the first member of an extended Toda lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptotic analysis to consider the long wavelength limits of the system. By considering various magnitudes for the parameters involved, we derive reduced equations related to the Korteweg-de Vries and potential Boussinesq equations.

Citation

Wattis, J. A., Gordoa, P. R., & Pickering, A. (2015). Behaviour of the extended Toda lattice. Communications in Nonlinear Science and Numerical Simulation, 28, https://doi.org/10.1016/j.cnsns.2015.04.006

• Journal Article Type: Article
• Publication Date: Apr 1, 2015
• Deposit Date: Jun 1, 2015
• Publicly Available Date: Jun 1, 2015
• Journal: Communications in Nonlinear Science and Numerical Simulation
• Print ISSN: 1007-5704
• Electronic ISSN: 1878-7274
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 28
• DOI: https://doi.org/10.1016/j.cnsns.2015.04.006
• Keywords: Nonlinear dynamics, Toda lattice, asymptotic behaviour, self-similar behaviour
• Public URL: https://nottingham-repository.worktribe.com/output/984448
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S1007570415001318