<i>λ</i>-Symmetry and <i>μ</i>-Symmetry Reductions and Invariant Solutions of Four Nonlinear Differential Equations

Abstract

On one hand, we construct λ-symmetries and their corresponding integrating factors and invariant solutions for two kinds of ordinary differential equations. On the other hand, we present μ-symmetries for a (2+1)-dimensional diffusion equation and derive group-reductions of a first-order partial differential equation. A few specific group invariant solutions of those two partial differential equations are constructed.

Keywords

• <i>λ</i>-symmetries
• <i>μ</i>-symmetries
• integrating factors
• invariant solutions