An asymptotic solution to non-linear transmission lines

This paper explores an asymptotic approach to the solution of a non-linear transmission line model. The model is based on a set of non-linear partial differential equations without analytical solution. The perturbations method is used to reduce the system of non-linear equations to a single non-linear partial differential equation, the modified Korteweg–de Vries equation (KdV). By using the Laplace transform, the solution is represented in integral form in terms of Green's functions. The solution for the non-linear case is obtained by means of asymptotic methods. Thus, an approximate explicit analytical solution to the problem is obtained where the errors can be controlled. This allows us to analyze the non-linear behavior of the solution. This kind of information is difficult to obtain by means of numerical methods due to the fact that for large periods of time greater computational resources are required and also accumulated errors increase. For this reason, asymptotic methods have a great importance like a natural complement to numerical methods. Computer simulations support the developments presented.