Expansions with respect to squares, symplectic and poisson structures associated with the Sturm–Liouville problem. II

The concept of tangent vector is made more precise to meet the specific nature of the Sturm–Liouville problem, and on this basis a Poisson bracket that is modified compared with the Gardner form by special boundary terms is derived from the Zakharov–Faddeev symplectic form. This bracket is nondegenerate, and in it the variables of the discrete and continuous spectra are separated.