Gap soliton of surface plasmon polaritons in left-handed material

We studied gap soliton of surface plasmon polaritons (SPPs) at an interface between vacuum and a Kerr nonlinear left-handed material (LHM). Applying multiple scale method, we derived the nonlinear coupled-mode equations for the gap soliton of SPPs. The linear gap is obtained and the bistable behavior of the transmissivity for the finite extend of the surface is presented.