β Scribed by V.A. Meshcheryakov; K.V. Rerikh
No coin nor oath required. For personal study only.
In the introduction the nonlinear system of functional equations for the matrix elements of the S-matrix is formulated, which we call the Chew-Low type equations. A short review of some papers devoted to equations of this type is given, and the advantages of the approach of the present paper are discussed.
In part II, Section 1 the transition to the projective coordinates in the space of the matrix elements of the S-matrix and the linearization of the unitarity conditions are performed.
An interpretation of the system of functional equations as a transformation in the (n -1) dimensional real space is given. It is shown that the some of the solutions of the initial system of equations are contained on the invariant hypersurfaces of this space (Section 2).
In Section 3 a method of the local construction of the invariant subspaces is proposed. In part III the method suggested is applied to the Chew-Low equations with the 3 x 3 crossing matrix. It is established that, if the Chew-Low equations possess a solution, then the arbitrariness of the solutions of the class (2.12), being the generalization of the familiar &arbitrariness, is not exhaustive.
π SIMILAR VOLUMES
## Communicated by H. Neunzert Stationary half-space solutions of the linearized Boltzmann equation are studied by energy estimates methods. We extend the results of Bardos, Caflisch and Nicolaenko for a gas of hard spheres to a general potential. Asymptotic behaviour is obtained for hard as well