Consider a PDE problem with two independent variables and one dependent variable, , and consider the list of infinitesimals of a symmetry group
In the input above you can also enter the symmetry without infinitesimals' labels, as in . The corresponding infinitesimal generator is
In canonical coordinates -say - the infinitesimals of this symmetry are . The transformation from the original variables to the canonical coordinates is obtained via
In the input above, instead of you can also pass the symmetry without infinitesimals' labels, as in . You can also pass the infinitesimal generator differential operator as first argument instead of the list of infinitesimals
Solving now for you can change variables in the infinitesimals or its corresponding differential operator using ChangeSymmetry, achieving the expected form
If is not indicated, variables prefixed by the underscore _ to represent the canonical variables are introduced
To obtain the output in any particular jet notation, useful to perform computations with objects of type, name, e.g., differentiation with respect to a function but represented by a name, use the jetnotation option; compare for instance the output (4.5) with the following output