Boundary conditions for integrable equations

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Abstract
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 maps it onto the boundary condition with linear dependence on t for the potentiated KdV.