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- Benjamin–Bona–Mahony_equation abstract "The Benjamin–Bona–Mahony equation (or BBM equation) – also known as the regularized long-wave equation (RLWE) – is the partial differential equationThis equation was studied in Benjamin, Bona, and Mahony (1972) as an improvement of the Korteweg–de Vries equation (KdV equation) for modeling long surface gravity waves of small amplitude – propagating uni-directionally in 1+1 dimensions. They show the stability and uniqueness of solutions to the BBM equation. This contrasts with the KdV equation, which is unstable in its high wavenumber components. Further, while the KdV equation has an infinite number of integrals of motion, the BBM equation only has three.Before, in 1966, this equation was introduced by Peregrine, in the study of undular bores.A higher-dimensional version is given bywhere is a fixed smooth function from to . Avrin & Goldstein (1985) proved local existence of a solution in all dimensions.".
- Benjamin–Bona–Mahony_equation thumbnail BBM_equation_-_overtaking_solitary_waves_animation.gif?width=300.
- Benjamin–Bona–Mahony_equation wikiPageID "16703476".
- Benjamin–Bona–Mahony_equation wikiPageRevisionID "605282084".
- Benjamin–Bona–Mahony_equation author1Link "Brooke Benjamin".
- Benjamin–Bona–Mahony_equation author2Link "Jerry L. Bona".
- Benjamin–Bona–Mahony_equation author3Link "John Joseph Mahony".
- Benjamin–Bona–Mahony_equation last "Benjamin".
- Benjamin–Bona–Mahony_equation last "Bona".
- Benjamin–Bona–Mahony_equation last "Mahony".
- Benjamin–Bona–Mahony_equation txt "yes".
- Benjamin–Bona–Mahony_equation year "1972".
- Benjamin–Bona–Mahony_equation subject Category:Differential_calculus.
- Benjamin–Bona–Mahony_equation subject Category:Equations_of_fluid_dynamics.
- Benjamin–Bona–Mahony_equation subject Category:Partial_differential_equations.
- Benjamin–Bona–Mahony_equation comment "The Benjamin–Bona–Mahony equation (or BBM equation) – also known as the regularized long-wave equation (RLWE) – is the partial differential equationThis equation was studied in Benjamin, Bona, and Mahony (1972) as an improvement of the Korteweg–de Vries equation (KdV equation) for modeling long surface gravity waves of small amplitude – propagating uni-directionally in 1+1 dimensions. They show the stability and uniqueness of solutions to the BBM equation.".
- Benjamin–Bona–Mahony_equation label "Benjamin–Bona–Mahony equation".
- Benjamin–Bona–Mahony_equation label "本杰明-博纳-马奥尼方程".
- Benjamin–Bona–Mahony_equation sameAs Benjamin%E2%80%93Bona%E2%80%93Mahony_equation.
- Benjamin–Bona–Mahony_equation sameAs Q4889468.
- Benjamin–Bona–Mahony_equation sameAs Q4889468.
- Benjamin–Bona–Mahony_equation wasDerivedFrom Benjamin–Bona–Mahony_equation?oldid=605282084.
- Benjamin–Bona–Mahony_equation depiction BBM_equation_-_overtaking_solitary_waves_animation.gif.
