Benjamin–Bona–Mahony equation
From Wikipedia, the free encyclopedia
The Benjamin–Bona–Mahony equation (or BBM equation) is the partial differential equation
This equation was introduced in (T. B. Benjamin, J. L. Bona & J. J. Mahony 1972) as an improvement of the KdV equation for modeling long waves of small amplitude in 1+1 dimensions.
A higher-dimensional version is given by
where φ is a fixed smooth function from 
to 
. Avrin & Goldstein (1985) proved local existence of a solution in all dimensions.
[edit] References
- Avrin, Joel & Goldstein, Jerome A. (1985), “Global existence for the Benjamin–Bona–Mahony equation in arbitrary dimensions.”, Nonlinear Anal. 9 (8): 861--865, MR0799889, DOI 10.1016/0362-546X(85)90023-9
- Benjamin, T. B.; Bona, J. L. & Mahony, J. J. (1972), “Model Equations for Long Waves in Nonlinear Dispersive Systems”, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 272 (1220): 47-78, ISSN 0962-8428, <http://www.jstor.org/stable/74079>
- Zwillinger, Daniel (1998), Handbook of differential equations (3rd ed.), Boston, MA: Academic Press, Inc., pp. 174, 176, MR0977062, ISBN 978-0127843964 (Warning: On p. 174 Zwillinger misstates the Benjamin-Bona-Mahony equation, confusing it with the similar KdV equation.)
