ABSTRACT
This chapter begins with the quasilinear hyperbolic system which governs the evolution of the current and charge distribution in the nonlinear transmission line and some analogies are drawn with certain aspects of the equations that govern the propagation, in one dimension, of plane waves in the wave-dielectric interaction problem. Prior to the work which appeared in the mid 1960’s, there appeared a series of papers by R. Landauer of IBM and his colleagues which considered the development and propagation of shock waves in nonlinear transmission lines and their effect on parametric amplification. The chapter discusses the problem of global existence of smooth solutions for the initial-value problem associated with the quasilinear system which governs the evolution of the current and charge distribution in a nonlinear transmission line.
