We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by a...

We investigate the nonlinear stage of the modulational (or Benjamin–Feir) instability by characterizing the initial value problem for the focusing nonlinear Schrödinger (NLS) equation with nonzero boundary conditions (NZBC) at infinity. We do so using the recently formulated inverse scattering transform (IST) for this problem. While the linearization of the NLS equation ceases to be valid when ...

By means of linear stability analysis (LSA) and direct numerical simulations the coupled Gross-Pitaevskii(GP)equations, we address impurity induced modulational instability (MI) associated nonlinear dynamics in Bose-Einstein condensates (BECs). We explore dual role played by impurities within BECs -- instigation MI dissipation initially generated solitary waves. Because impurities, repulsive ar...

We calculate the growth rate of the small-amplitude perturbations superimposed on a one-dimensional soliton that is fully coherent in the self-trapping dimension, yet uniform and partially incoherent in the other transverse dimension. Such solitons become transversely stable only if the correlation distance is below a specific threshold value. We show that this threshold for transverse instabil...

Abstract. The modulational instability of two interacting waves in a nonlocal Kerrtype medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero groupvelocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity m...

We analyze stability of the TM polarized optical solitons and nonlinear guided waves localized at a metal-dielectric interface. We demonstrate, both analytically and numerically, that the spatial solitons can experience vectorial transverse modulational instability that leads to the generation of arrays of two-dimensional TM polarized self-trapped localized beams. In a sharp contrast, we reveal...

We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schrödinger equation involving local, arbitrary nonlinear responses to the applied field. In particular, our theory accounts for the recently proposed higher-order Kerr nonlinearities, providing very simple analytical criteria for the identification of mul...