Evolution of the Main Signal

Abstract

This chapter obtains the contribution A_c(z, t) to the asymptotic behavior of the propagated field A_cz, t) that is due to the presence of any simple pole singularities of the spectral function ũ(ω — ω_c). The field A_c(z, t) is associated with any long term signal being propagated. The velocity of propagation of the signal and the transition from the precursor field to the signal field are determined by the relative importance of the component fields A _s (z, t), A _B (z, t), and A _c (z,t). Hence, discussion of those topics is deferred to Chap. 9 which deals with the evolution of the total field A(z,t) by combining the results of this chapter with those of Chap. 7.