Group analysis of the one-dimensional boltzmann equation: II. Equivalence groups and symmetry groups in the special case |
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Authors: | K S Platonova |
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Institution: | 1.Lomonosov Moscow State University,Moscow,Russia |
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Abstract: | We obtain relations that define the equivalence algebra of the family of one-dimensional Boltzmann equations f t + cf x + F(t, x, c)f c = 0 and show that all equations of that form are locally equivalent. We carry out the group classification of the equation with respect to the function F in the special case where the function F and the transformations of the variables t and x are assumed to be independent of c. We show that, under such constraints for the transformation and the family of equations, the maximum possible symmetry algebra is eight-dimensional, which corresponds to an equation with a linear function F. |
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