Periodic and chaotic behaviour in a reduction of the perturbed Korteweg-de Vries equation
- 8 April 1994
- journal article
- Published by The Royal Society in Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- Vol. 445 (1923), 1-21
- https://doi.org/10.1098/rspa.1994.0045
Abstract
The dynamical behaviour of a reduction of the forced (and damped) Korteweg-de Vries equation is studied numerically. Chaos arising from subharmonic instability and homoclinic crossings are observed. Both period-doubling bifurcations and the Melnikov sequence of subharmonic bifurcations are found and lead to chaotic behaviour, here characterised by a positive Lyapunov exponent. Supporting theoretical analysis includes the construction of periodic solutions and homoclinic orbits, and their behaviour under perturbation using Melnikov functions.Keywords
This publication has 23 references indexed in Scilit:
- Dynamical chaos of solitons and nonlinear periodic wavesPhysics Reports, 1989
- Resonant flow of a stratified fluid over topographyJournal of Fluid Mechanics, 1986
- The evolution of resonant water-wave oscillationsJournal of Fluid Mechanics, 1986
- Universal behavior in nonlinear systemsPhysica D: Nonlinear Phenomena, 1983
- Regular and Stochastic MotionPublished by Springer Science and Business Media LLC ,1983
- Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced OscillationsPublished by Defense Technical Information Center (DTIC) ,1981
- An example of bifurcation to homoclinic orbitsJournal of Differential Equations, 1980
- The onset spectrum of turbulencePhysics Letters A, 1979
- Resonant oscillations of water waves I. TheoryProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1968
- On cnoidal waves and boresProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1954