Lie symmetry analysis, conservation laws and exact solutions of the generalized time fractional Burgers equation

Abstract

Under investigation in this work are the invariance properties of the generalized time fractional Burgers equation, which can be used to describe the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Lie group analysis method is applied to consider its vector fields and symmetry reductions. Furthermore, based on the sub-equation method, a new type of explicit solutions for the equation is well constructed with a detailed analysis. By means of the power series theory, exact power series solutions of the equation are also constructed. Finally, by using the new conservation theorem, conservation laws of the equation are well constructed with a detailed derivation.