Benjamin–Bona–Mahony equation

The Benjamin–Bona–Mahony equation (BBM equation, also regularized long-wave equation; RLWE) is the partial differential equation u t + u x + u u x − u x x t = 0. {\displaystyle u_{t}+u_{x}+uu_{x}-u_{xxt}=0.\,} This 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.

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