Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation

Abstract

We consider a general class of variable coefficient Calogero-Degasperis equations. The complete Lie group classification is performed with the aid of the appropriate equivalence group. Lie symmetries are used to derive a number of reductions by constructing the corresponding optimal lists of one-dimensional subalgebras of the Lie symmetry algebras. Furthermore, a number of non-Lie reductions are given. One of the reduced equations is the variable coefficient potential KdV equation which is studied from the point of view of Lie group analysis.

Transformation Properties of a Class of Variable Coefficient Boiti–Leon–Manna–Pempinelli Equations

“…Lie symmetries of a similar equation are presented in [16]. The Lie symmetry X 3 + X 2 leads to the reduction…”

“…In this approach, we require invariance of Equation (10) in conjunction with the invariant surface condition (12) under the infinitesimal transformations generated by the Lie operator (11). Motivated by the work in reference [16], we state that, for Equation (10), we can search for three forms of reduction operators:…”

The Lie symmetry approach on (1+2)-dimensional financial models

“…However, the equivalence transformations admitted by the class is a great tool to simplify the analysis. For more details of this method one can see, for example, in [17,18] and a recent example of group classification for a class of (1+2) equations can be found in [19].…”