Modulational instability in a nonlinear transmission line

The paper investigates the instability of the sidebands about the amplitude-modulated wave propagating along a nonlinear transmission line described by the nonlinear Schrodinger equation, i¿¿1, + p¿¿xx + q|¿¿|2¿¿ = 0, where both coefficients p and q are positive, the instability for the sidebands is investigated. The instability condition is expressed by a relationship between amplitude of carrier wave V and wavenumber of modulated wave K. When an inequality, K < ¿¿(2q/p)|V|, is satisfied, the system is unstable. Furthermore, the growth rate of the modulated wave, namely the increase of the modulational ratio, is calculated using a simple method. The maximum value of the growth rate is also found.