Asymmetrical solitary waves in coupled nonlinear transmission lines

Abstract

Asymmetrical solitary waves are characterized in symmetrical, capacitively coupled transmission lines, called coupled nonlinear transmission lines (NLTLs), which are periodically loaded with Schottky varactors, in order to amplify short electrical pulses. In this work, the transmission equations of coupled NLTLs are numerically solved, using two symmetrical Korteweg–de Vries (KdV) systems with linear dispersionless coupling, to show that the lines exhibit symmetry breaking in order to support asymmetrical solitary waves. In particular, two interacting solitary waves with different polarities are investigated. The KdV systems show that the polarities of the preceding and the subsequent waves in coupled NLTLs are interchanged through colliding interactions. The process is quantified in the framework of reduction theory, assuming small velocity differences and interaction strength between the two waves. In addition, results show that the leading wave gains amplitude via collision, which means that coupled NLTLs provide good platforms for amplifying short electrical pulses.