Quasiperiodic Multicolor Solitons in Quasi-Phase-Matched Quadratic Media

We study the (1+1)-dimensional quasiperiodic multicolor solitons due to cascading quadratic nonlinear response in generalized one-dimensional quasiperiodic optical superlattice waveguides and show that the dynamic equations describing the quasi-phase-matched multicolor solitons include quasiperiodicity-induced Kerr effects, such as self- and cross-phase modulation, third harmonic generation and four-wave mixing. We demonstrate the stability of this multicolor solitons by means of a Lyapunov analysis based on the energy integral of the wave coupling equations and investigate the dynamics of the multicolor solitons using a virial identity, which predicts a stable propagation of the mutually trapped solitons. We finally establish the analytic stability criterion for the multicolor solitons by applying a multiscale asymptotic method.