Symmetry Reductions, Exact Solutions and Conservation Laws for the Coupled Nonlinear Klein-Gordon System

The Lie group method is applied to a coupled nonlinear Klein-Gordon system. The Klein-Gordon system is used to model many nonlinear phenomena including the propagation of dislocations in crystals and the behavior of elementary particles and the propagation of fluxons in Josephson junctions. The symmetry reductions and exact solutions which include the stationary and solitary waves are obtained. In addition, by using the multiplier method, we derive the local conservation laws of the coupled nonlinear Klein-Gordon system.