text: The Benjamin–Bona–Mahony equation (BBM equation), or regularised long wave (RLW) equation, is in dimensional form given by:
  All quantities have the same meaning as for the KdV equation. The BBM equation is often preferred over the KdV equation because it has a better short-wave behaviour.
  ; Derivation
  The derivation is analogous to the one for the KdV equation.  The dimensionless BBM equation is, non-dimensionalised using mean water depth h and gravitational acceleration g:
  This can be brought into the standard form
  through the transformation:
  :    and  
  but this standard form will not be used here.
  Analogue to the derivation of the cnoidal wave solution for the KdV equation, periodic wave solutions η(ξ), with ξ = x−ct are considered Then the BBM equation becomes a third-order ordinary differential equation, which can be integrated twice, to obtain:
  :  with  
  Which only differs from the equation for the KdV equation through the factor c in front of () in the left hand side.  Through a coordinate transformation β = ξ /  the factor c may be removed, resulting in the same first-order ordinary differential equation for both the KdV and BBM equation.  However, here the form given in the preceding equation is used.  This results in a different formulation for Δ as found for the KdV equation:
  The relation of the wavelength λ, as a function of H and m, is affected by this change in 
  For the rest, the derivation is analogous to the one for the KdV equation, and will not be repeated here.
  ; Résumé
  The results are presented in dimensional form, for water waves on a fluid layer of depth h.
  The cnoidal wave solution of the BBM equation, together with the associated relationships for the parameters is:
  The only difference with the cnoidal wave solution of the KdV equation is in the equation for the wavelength λ.  For practical applications, usually the water depth h, wave height H, gravitational acceleration g, and either the wavelength λ, or—most often—the period (physics) τ are provided. Then the elliptic parameter m has to be determined from the above relations for λ, c and τ through some iterative method.