Stationary Eigenmodes and Their Stability during Wave Propagation in a Medium with Quadratic and Cubic Nonlinearities without Dispersion

摘要

Stationary eigenmodes are derived for wave propagation in a medium with quadratic and cubic nonlinearities. Aperiodic algebraic solitary waves are the eigenmodes with a continuous spectrum while periodic solitary waves are those with a spectrum comprising an infinite number of harmonics. Stationary eigenmodes comprising the fundamental and the second harmonic only have also been derived. The stability of the aperiodic solitary waves have been studied numerically and a stabilization technique proposed. The stability of stationary eigenmodes for the two-frequency case is also discussed. Keywords: Nonlinear Klein-Gordon. (kr)