Similarity Solutions of Systems of Partial Differential Equations Using Macsyma

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Similarity Solutions of Systems of Partial Differential Equations Using Macsyma
P Rosenau
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This, as explained in [1], is a sufficient but not a necessary condition. The coefficients of the S 's m are differential equations satisfied by the infinitesimal generators (X, T, U); these are the determining equations mentioned earlier. In practice the determining equations usually can be solved easily, as they are an overdetermined set of linear equations. A knowledge of the infinitesimal transformations enables one to construct a continuous transformation or in turn to find the invariants ...of the group that serve as the new de- pendent and independent variable. It is in these new variables that Eqs. (1) exhibit their symruetry and result in a re- duction by one in the number of independent variables.
To illustrate the desirability of using MACSYMA to calcu- late the determining equations, suppose a partial differential equation contains a derivative t — (assume scalar u and x) .
o X In terms of the new variables, the transformed partial differential 3u ' equation contains a term r • But from Eq.


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