Lie Symmetry Analysis of a Third-Order Equation Arising from a General Class of Lotka–Volterra Chains

Abstract

In the literature has recently appeared a class of bi-cubic equations from the study of a general class of Lotka–Volterra chains. Lie symmetry analysis is performed for this non-linear partial differential equation and a list of similarity reductions is presented with the employment of the appropriate optimal system. This family of bi-cubic equations can be generalized by taking the parameters as functions of time or as functions of the space variable x. The corresponding symmetry analysis for these two general cases is also presented.