KdV方程式
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.