Lie symmetry analysis, optimal system, symmetry reductions and analytic solutions for a (2＋1)-dimensional generalized nonlinear evolution system in a fluid or a plasma

Abstract

Nonlinear evolution equations are used to describe such nonlinear phenomena as the solitons, travelling waves and breathers in fluid mechanics, plasma physics and optics. In this paper, we investigate a (2＋1)-dimensional generalized nonlinear evolution system in a fluid or a plasma. Via the Lie symmetry analysis, we acquire the Lie point symmetry generators and Lie symmetry groups of that system. Via the optimal system method, we derive the optimal system of the 1-dimensional subalgebras. Based on the symmetry generators in that optimal system, we give some symmetry reductions for the (2＋1)-dimensional generalized nonlinear evolution system. Finally, via those symmetry reductions, we acquire some soliton, rational-type and power-series solutions.