Solution of quantum Gel'fand–Levitan–Marchenko equations for the sine-gordon model in the soliton sector for $\gamma=\pi/\nu$

The solutions of the quantum Gel' fand–Levitan–Marehenko equations for the sine-Gordon model are studied in the sector containing solitons. The case $\gamma=\pi/\nu$ ($\nu$ integer), when there is no soliton reflection, is considered. A recursive procedure for constructing solutions is obtained, and examples in sectors containing a small number of solitons are considered.