Benjamin–Bona–Mahony equation
- Benjamin–Bona–Mahony equation
The Benjamin–Bona–Mahony equation (or BBM equation) is the partial differential equation
:
This equation was introduced in harvs| author1-link=Brooke Benjamin|first= T. B. |last=Benjamin|first2= J. L.|last2= Bona |first3=J. J.|last3= Mahony|year=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 is a fixed smooth function from to . harvtxt|Avrin|Goldstein|1985 proved local existence of a solution in all dimensions.
References
*citation|doi=10.1016/0362-546X(85)90023-9|id=MR|0799889
last=Avrin|first=Joel|last2= Goldstein|first2= Jerome A.
title=Global existence for the Benjamin–Bona–Mahony equation in arbitrary dimensions.
journal=Nonlinear Anal.|volume= 9 |year=1985|issue= 8|pages= 861--865
*citation|title=Model Equations for Long Waves in Nonlinear Dispersive Systems
first= T. B. |last=Benjamin |authorlink=Brooke Benjamin |first2= J. L.|last2= Bona |first3=J. J.|last3= Mahony
journal=Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences|volume= 272|issue= 1220 |year= 1972|pages= 47-78
url= http://www.jstor.org/stable/74079|ISSN =0962-8428
*citation|id=MR|0977062
last=Zwillinger|first= Daniel
title=Handbook of differential equations|publisher= Academic Press, Inc.|place= Boston, MA|edition=3rd|year= 1998|ISBN= 978-0127843964|pages=174, 176 (Warning: On p. 174 Zwillinger misstates the Benjamin-Bona-Mahony equation, confusing it with the similar KdV equation.)
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