In the paper, we derive a geometric meshless method for coupled nonlinear sine-Gordon (CNSG) equations. Approximate solutions of the CNSG equations are supposed to be expressed as the moving Kriging (MK) shape functions in the space direction. Global weak form of the CNSG equations is obtained, and then, a system of ODEs in time coordinate is extracted after imposing the MK meshless method. Then the geometric integrator, namely group preserving scheme, is offered to approximate the solution of obtained system of ODEs. Stability analysis of the method is numerically investigated. Numerical experiments show that the proposed method is effective and accurate for the CNSG equations.
