Vector-Resonance-Multimode Instability

Vector-Resonance-Multimode Instability.

The modulation and multimode instabilities are the main mechanisms which drive spontaneous spatial and temporal pattern formation in a vast number of nonlinear systems ranging from biology to laser physics. Using an Er-doped fiber laser as a test bed, here for the first time we demonstrate both experimentally and theoretically a new type of a low-threshold vector-resonance-multimode instability...

RELATIONSHIP OF THE MULTIMODE KINK INSTABILITY TO d-SPOT FORMATION

We study the current-driven kink instability with a three-dimensional MHD spectral code, under conditions appropriate for the convection zone of the Sun. Our goal is to determine whether the kink instability can explain the unusual morphology of certain ““ d-spot ÏÏ active regions. The characteristics of these d-spots are unusually large tilt upon emergence, subsequent rotation, compactness dur...

Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers

Resonance and marginal instability of switching systems

We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of Chitour, Mason, and Sigalotti (2012) stating that for generic systems, the resonance is sufficient for marginal instability and for polynomial growth of the...

Relation between Periodic Soliton Resonance and Instability

There are periodic soliton resonances in interactions between two periodic solitons and between periodic soliton and another kind of soliton. A close relation exists between the periodic soliton resonance and soliton instability to transverse disturbances. It is shown that the instability occurred in the line soliton is relaxed by emission of the periodic soliton and the periodic soliton resona...