Inverse Spectral Problem for the Periodic Camassa-Holm Equation

We consider the direct/inverse spectral problem for the periodic Camassa-Holm equation. In fact, we survey the direct/inverse spectral problem for the periodic weighted operator Ly = m -1 (-y + 1 4 y) acting in the space L 2 (R, m(x)dx), where m = u xx -u > 0 is a 1-periodic positive function and u is the solution of the Camassa-Holm equation

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