Explicit determination of isovector fields of equivalence groups for balance equations of arbitrary order—Part II

Abstract

The explicit solutions of previously given determining equations for isovector components (infinitesimal generators) associated with Lie groups of equivalence transformations for the most general family of balance equations of arbitrary order involving arbitrary but finite number of independent and dependent variables are provided. Equivalence transformations which are considered in this work map the solutions of partial differential equations containing arbitrary functions or parameters to the solutions of the equations of the same structure but with different functions or parameters. The general solutions exposed here are employed to determine the isovector fields corresponding to a sort of Korteweg–de Vries type equation involving third derivative with respect to spatial variable.