Solution of quantum Gel'fand–Levitan–Marchenko equations for the sine-Gordon model with $\gamma=\pi/\nu$

General solution of quantum Gelfand–Levitan–Marchenko equations for sine-Gordon model with $\gamma=\pi/\nu$ ($\nu$ being integer) is obtained. Matrix elements of operators $ехр(\pm i\sqrt{2\gamma}\times u(x_0, x_1))$ between the vacuum and arbitrary state are calculated. The series for two-point Green functions are obtained. The coincidence with the case of free massive Fermi field for $\gamma=\pi/2$ is verified. The possibility of obtaining similar formulas for other local operators is discussed.