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We propose an expression for the classical limit of diagonal form factors inwhich we integrate the corresponding observable over the moduli space ofclassical solutions. In infinite volume the integral has to be regularized byproper subtractions and we present the one, which corresponds to the classicallimit of the connected diagonal form factors. In finite volume the integral isfinite and can be expressed in terms of the classical infinite volume diagonalform factors and subvolumes of the moduli space. We analyze carefully theperiodicity properties of the finite volume moduli space and found a classicalanalogue of the Bethe-Yang equations. By applying the results to theheavy-heavy-light three point functions we can express their strong couplinglimit in terms of the classical limit of the sine-Gordon diagonal form factors.

Classical limit of diagonal form factors and HHL correlators