Wave-action transport for a variable-speed wave
= Wave-action transport for a variable-speed wave
{title2=$(\omega A^2)_T+\nabla\cdot(c^2\mathbf kA^2)=0$}
The first-order imaginary balance of the <wave equation> in <geometrical optics> gives $\partial_T(\omega A^2)+\nabla\cdot(c^2\mathbf k A^2)=0$ for a real leading <amplitude>. The action density $\omega A^2$ travels with the <group velocity> $c^2\mathbf k/\omega$. For a complex <amplitude> replace $A^2$ by $|A|^2$.