Integrable Bogoliubov Transform and Integrable Model

By defining Bogoliubov transform as a function of parameters, the integrability of the Bogoliubov transform in parameter space is investigated. It is shown that integrable Bogoliubov transform is closely related to the known integrable model. The relation between the integrable Bogoliubov transform and geometric phase of vacuum induced by the Bogoliubov transform is also discussed.