Exact transverse solitary and periodic wave solutions in a coupled nonlinear inductor-capacitor network

Through two methods, we investigate the solitary and periodic wave solutions of the differential equation describing a nonlinear coupled two-dimensional discrete electrical lattice. The fixed points of our model equation are examined and the bifurcations of phase portraits of this equation for various values of the front wave velocity are presented. Using the sine-Gordon expansion method and classic integration, we obtain exact transverse solutions including breathers, bright solitons, and periodic solutions.