Finding non-local and contact/dynamical symmetries of Riccati chain

Abstract

In this work, we present a new approach to find non-local symmetries and contact symmetries from the admitted Lie point symmetries of the considered system of nonlinear differential equations. By introducing a new function in both the numerator and denominator in the relation which relates the \(\lambda \)-symmetry function and the Lie point symmetry characteristics, we generate non-local symmetries as well as contact symmetries. To do so, we have to define another function \(g_3\) and then we identify two different cases, where the function \(g_3=0\) and \(g_3 \ne 0\). To validate the results, we consider the Ricatti chain as an example and find the non-local and contact symmetries admitted by the first four of the underlying equations. We also find the contact symmetries admitted by the well-known Mathews–Lakshmanan oscillator equation.