Exact <i>N</i>-Soliton Solution of a Nonlinear Lumped Network Equation

Abstract

Exact N -soliton solutions have been obtained for the nonlinear lumped network equation, \(\frac{\partial^{2}}{\partial t^{2}}\log(1+V_{n}(t)){=}V_{n+1}(t)+V_{n-1}(t)-2V_{n}(t)\). The solutions have the same functional forms as the N -soliton solution of the Korteweg-de Vries equation.