Equivalence Classes and Symmetries of the Variable Coefficient Kadomtsev—Petviashvili Equation

We classify the variable coefficient Kadomtsev—Petviashvili (VCKP) equation into equivalence classes under the group of local point transformations, leaving the equation form invariant but changing the coefficient functions. We list the representatives of all equivalence classes with the corresponding transformations. Then, we obtain the symmetry group of the VCKP equation and in particular discuss how to use these transformations to classify low-dimensional symmetry algebras in the generic case. We conclude with a discussion of the implications of the present article.