Zero-curvature condition
= Zero-curvature condition
= Zero-curvature representation
{synonym}
For $\Phi_x+U\Phi=0$ and $\Phi_y+V\Phi=0$, compatibility is $V_x-U_y+[U,V]=0$.
For the auxiliary equations $\psi_x=U\psi$ and $\psi_t=V\psi$, equality of mixed derivatives gives $U_t-V_x+[U,V]=0$. This is the compatibility condition for a <Lax pair>.