Some operators which commute in a nonlinear Boltzmann equation

A two parameter semigroup of linear operators in a Hilbert space is shown to commute in the Tjon-Wu model Boltzmann equation (TW equation). Under appropriate conditions on the parameters the operator is of Hilbert-Schmidt type. In this case, it generates new solutions of the TW equation from known ones; and different existence domains can be derived from those already established. Analogous transformations may be obtained for other Boltzmann equations which are related to the TW equation via integral transforms. (author)