Group analysis of the one-dimensional Boltzmann equation: IV. Complete group classification in the general caseстатья
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Аннотация:We consider the one-dimensional Boltzmann equation ft + cfx + (Ff)c = 0 with a function F depending
on (t, x, c, f) and obtain the complete group classification of such equations in the class of point change of whole set of variables (t, x, c, f). For this, we impose additional conditions on the transformations for the invariance of (a) the relations dx = c dt and dc = F dt, (b) the lines dt = dx = 0, and (c) the form fdxdc, which fix the physical meaning of the used variables and the relations between them.