Elastic Interaction and Conservation Laws for the Nonlinear Self-Dual Network Equation in Electric Circuit

The nonlinear self-dual network equation can describe the propagation of electrical signals in electric circuit. In this paper, the nonlinear self-dual network equation is investigated via Darboux transformation (DT) technique. $N$-fold DT and conservation laws for the nonlinear self-dual network equation are constructed on the basis of its Lax representation. $N$-soliton solutions in terms of determinant are derived with the resulting DT. Structures of the one-, two-, and three-soliton solutions are shown graphically. Elastic interaction phenomena between/among the two and three solitons are discussed for the nonlinear self-dual network equation, which might be helpful to understanding the propagation of electrical signals.