Search results for "Swift–Hohenberg equation"
showing 3 items of 3 documents
Generalized complex Swift-Hohenberg equation for optical parametric oscillators
1997
A generalized complex Swift-Hohenberg equation including diffraction and nonlinear resonance terms is derived for spatially extended nondegenerate optical parametric oscillators (OPOs) with flat end mirrors. For vanishing pump detuning this equation becomes the complex Swift-Hohenberg (SH) equation valid also for lasers. Nevertheless the similarities between OPOs and lasers are limited, since the diffractive character of OPOs is lost when the diffraction coefficients of signal and idler fields are equal. This manifests, e.g., in the absence of advection by traveling waves (TWs), a clear difference with lasers. When pump detuning is nonzero a nonlinear resonance develops, as it occurs in deg…
Stability of localized structures in the Swift-Hohenberg equation.
1999
We show that nonmonotonic (oscillatory) decay of the boundaries of phase domains is crucial for the stability of localized structures in systems described by Swift-Hohenberg equation. The less damped (more oscillatory) are the boundaries, the larger are the existence ranges of the localized structures. For very weakly damped spatial oscillations, higher-order localized structures are possible.
Dynamics of phase domains in the Swift-Hohenberg equation
1998
Abstract We analyze analytically and numerically the dynamics of phase domains in the Swift-Hohenberg equation. For negative or small positive detuning domains contract and disappear. A large positive detuning leads to dendritic growth of the domains, and the formation of labyrinth structures. Intermediate detuning results in stable circular domains - the localized structures of the Swift-Hohenberg equation. The predicted phenomena should occur in parametrically driven chemical, hydrodynamical, and nonlinear optical systems.