Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations

Wattis, Jonathan A.D.; Gordoa, PIlar; Pickering, Andrew

Abstract

We consider the first member of an extended modified Volterra 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 modified Korteweg-de Vries and nonlinear Schrodinger equations.

Citation

Wattis, J. A., Gordoa, P., & Pickering, A. (2018). Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations. Communications in Nonlinear Science and Numerical Simulation, 65, 98-110. doi:10.1016/j.cnsns.2018.05.016

• Journal Article Type: Article
• Acceptance Date: May 18, 2018
• Online Publication Date: May 19, 2018
• Publication Date: Dec 1, 2018
• Deposit Date: May 18, 2018
• Publicly Available Date: May 20, 2019
• Journal: Communications in Nonlinear Science and Numerical Simulation
• Print ISSN: 1007-5704
• Electronic ISSN: 1007-5704
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 65
• Pages: 98-110
• DOI: https://doi.org/10.1016/j.cnsns.2018.05.016
• Keywords: nonlinear dynamics, modified Volterra lattice, asymptoticbehaviour, integrable systems
• Public URL: http://eprints.nottingham.ac.uk/id/eprint/51874
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S1007570418301606
• Copyright Statement: Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0