Linear dispersive Stokes equation
= Linear dispersive Stokes equation
{title2=$u_t+u_x+u_{xxx}=0$}
= Stokes dispersive equation
{c}
{synonym}
The scalar <linear partial differential equation> $u_t+u_x+u_{xxx}=0$ is an <Airy equation> with a first-order transport term. It is a linearization of the <Korteweg-De Vries equation> with an advective term retained. It is distinct from the viscous incompressible-flow <Stokes equation>. On the whole line its spatial <Fourier transform> evolves by $e^{i(k^3-k)t}$.