A mathematical model for long waves generated by wavemakers in non-linear dispersive systems
- 1 March 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 73 (2) , 391-405
- https://doi.org/10.1017/s0305004100076945
Abstract
An initial-boundary-value problem for the equationis considered for x, t ≥ 0. This system is a model for long water waves of small but finite amplitude, generated in a uniform open channel by a wavemaker at one end. It is shown that, in contrast to an alternative, more familiar model using the Korteweg–deVries equation, the solution of (a) has good mathematical properties: in particular, the problem is well set in Hadamard's classical sense that solutions corresponding to given initial data exist, are unique, and depend continuously on the specified data.Keywords
This publication has 2 references indexed in Scilit:
- Model equations for long waves in nonlinear dispersive systemsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1972
- XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wavesJournal of Computers in Education, 1895