Ninth-order dispersive advection equation
= Ninth-order dispersive advection equation
For
$$
\phi_t+U\phi_x+\frac19\phi_{xxxxxxxxx}=0,
$$
the dispersion relation is $\omega=Uk+k^9/9$, so $c_p=U+k^8/9$ and $c_g=U+k^8$.
= Ninth-order dispersive advection equation
For
$$
\phi_t+U\phi_x+\frac19\phi_{xxxxxxxxx}=0,
$$
the dispersion relation is $\omega=Uk+k^9/9$, so $c_p=U+k^8/9$ and $c_g=U+k^8$.