Solitary wave solutions for a model of the two-way propagation of water waves in a channel
- 1 September 1981
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 90 (2) , 343-360
- https://doi.org/10.1017/s0305004100058801
Abstract
Bona and Smith (6) have suggested that the coupled system of equations has the same formal justification as other Boussinesq-type models for the two-way propagation of one-dimensional water waves of small but finite amplitude in a channel with a flat bottom. The variables u and η represent the velocity and elevation of the free surface, respectively. Using the energy invariant they show that for a restricted, but nevertheless physically relevant, class of initial data, the system (1·1) has solutions which exist for all time, and that in such circumstances the wave height is bounded solely in terms of the initial data.This publication has 4 references indexed in Scilit:
- Bifurcation for variational problems when the linearisation has no eigenvaluesJournal of Functional Analysis, 1980
- Bifurcation for Neumann problems without eigenvaluesJournal of Differential Equations, 1980
- A model for the two-way propagation of water waves in a channelMathematical Proceedings of the Cambridge Philosophical Society, 1976
- Some global results for nonlinear eigenvalue problemsJournal of Functional Analysis, 1971