Partial Differential Equations in Applied Mathematics (Jun 2023)
On the form of Lie symmetries of systems with three pdes: The examples of two variable coefficient Hirota Satsuma systems
Abstract
We consider a general class of systems of three partial differential equations and we provide restrictions on the form of Lie symmetry operators admitted by such systems. When these restrictions are known in advance, the symmetry analysis becomes simpler. Special cases of this class are two generalizations of Hirota–Satsuma systems with variable coefficients. We derive the equivalence groups for these two systems. With the aid of the equivalence groups and the restricted form of the Lie symmetry operators, we present an enhanced Lie group classification for the two Hirota–Satsuma systems. For each class a specific system is single out which has the property to be mapped into a constant coefficient system.
