with "ω" the angular frequency and "k" the wavenumber. not surprisingly, this is of similar form as the one for the korteweg–de vries equation, provided "κ" is non-zero. for "κ" equal to zero, the camassa–holm equation has no frequency dispersion — moreover, the linear phase speed is zero for this case. as a result, "κ" is the phase speed for the long-wave limit of "k" approaching zero, and the camassa–holm equation is (if "κ" is non-zero) a model for one-directional wave propagation like the korteweg–de vries equation.