A model for the two-way propagation of water waves in a channel
- 1 January 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 79 (1), 167-182
- https://doi.org/10.1017/s030500410005218x
Abstract
Global existence, uniqueness and regularity of solutions and continuous dependence of solutions on varied initial data are established for the initial-value problem for the coupled system of equationsThis system has the same formal justification as a model for the two-way propagation of (one-dimensional) long waves of small but finite amplitude in an open channel of water of constant depth as other versions of the Boussinesq equations. A feature of the analysis is that bounds on the wave amplitude η are obtained which are valid for all time.Keywords
This publication has 7 references indexed in Scilit:
- The initial-value problem for the Korteweg-de Vries equationPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1975
- A numerical simulation of the undular hydraulic jumpJournal of Hydraulic Research, 1974
- Model equations for long waves in nonlinear dispersive systemsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1972
- An integral equation for unsteady surface waves and a comment on the Boussinesq equationJournal of Fluid Mechanics, 1971
- Functional AnalysisPublished by Springer Nature ,1971
- The transformation of a solitary wave over an uneven bottomJournal of Fluid Mechanics, 1969
- The initial-value problem for long waves of finite amplitudeJournal of Fluid Mechanics, 1964