Gap solitons in nonlinear electrical transmission lines

Abstract

We study theoretically and numerically the properties of monochromatic waves in a nonlinear electrical transmission line,whose capacitance has a periodic spatial variation.ln the continuum limit and weak amplitude limit we reduce the characteristic equations of this system to NLS equation. We find analytical solutions for the voltage envelope, which propagate with frequency in the gap induced by the capacitance periodicity. Our numerical experiments show that, when the input voltage increases, the transmissivity in the gap increases and the voltage envelope approaches the stationnary shape predicted by theory.