Exact similarity solutions and classification of symmetries for Carleman-Boltzmann Equation

Abstract

In this paper, we show that the symmetry algebra admitted by the CarlemanBoltzmann equation is solvable, not semi simple and not nilpotent. Furthermore, by applying the Ovsiannikov’s approach, we construct one, two and three dimensional optimal systems. Based on the structurally important informations containing in the obtained optimal systems, we construct numerous reduction equations and we get some exact solutions.