Boundary conditions for integrable equations

The problem of constructing boundary conditions for nonlinear equations compatible with higher symmetries is considered. In particular, this problem is discussed for the sine-Gordon, Jiber-Shabat, Liouville and KdV equations. New results are obtained for the last two ones. The boundary condition for the KdV contains two arbitrary constants. The substitution u = qx maps it onto the boundary condition with linear dependence on t for the potentiated KdV