Search results for "Pattern"
showing 10 items of 4203 documents
A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two
2008
Abstract We suggest how one can obtain exact solutions of some type of coupled Korteweg–de Vries equations by means of hyperelliptic functions of genus two.
Multiparticle breathers for a chain with double-quadratic on-site potential
1999
We investigate the existence and properties of multiparticle breathers for a one-dimensional model with harmonic nearest neighbor interactions where a group of r particles $(r=1,2,3,\dots{})$ perform interwell oscillations between both wells of a double-quadratic on-site potiential. We find two types of such breathers. For the first type the breather frequency $\ensuremath{\Omega}$ is within the single-particle oscillator spectrum, and the ``residence'' time of each breather particle in the left and right well is about the same. For the second breather $\ensuremath{\Omega}$ is below that spectrum, and the ratio ${\ensuremath{\tau}}_{L}/{\ensuremath{\tau}}_{R}$ of the residence time in the l…
Dissipative structures in optomechanical cavities
2012
Motivated by the increasing interest in the properties of multimode optomechanical devices, here we study a system in which a driven mode of a large-area optical cavity is despersively coupled to a deformable mechanical element. Two different models naturally appear in such scenario, for which we predict the formation of periodic patterns, localized structures (cavity solitons), and domain walls, among other complex nonlinear phenomena. Further, we propose a realistic design based on intracavity membranes where our models can be studied experimentally. Apart from its relevance to the field of nonlinear optics, the results put forward here are a necessary step towards understanding the quant…
Spatial localization and pattern formation in discrete optomechanical cavities and arrays
2020
We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig & Marquardt [Phys. Rev. Lett. 101, 073603 (2013)]. Also, we study the connections between both types of models and continuous OM models. While all three types of models merge naturally in the limit of a large number of densely distribu…
Effective kink-kink interaction in a one-dimensional model mediated by phonon exchange
1994
The general 1D double-well model with anharmonic interaction is considered in the displacive limit. Expansion of the Hamiltonian around a multikink state results in a phonon-kink Hamiltonian. It is shown that at rather low temperatures and short wave lengths the phonon-kink interaction can be treated in Born approximation, leading to a decomposition of the multikink-phonon Hamiltionian. Elimination of the phonons results in an effective potential for the kink-kink interaction, which corresponds to the one-dimensional analog of the RKKY interaction. This long-range interaction is inherent only for models with anharmonic on-site potentials and not in case of a double-parabola model.
Numerical study of the stability of the Peregrine solution
2017
International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.
Coherent light scattering on nanofluids: computer simulation results.
2008
If coherent light is incident on a suspension containing nanoparticles, they act as scattering centers and the result of the far-field interference is a "speckled" image. The scattering centers have a complex movement of both sedimentation and Brownian motion. Consequently the speckle image is not static but presents time fluctuations. A computer code to simulate the dynamics of the coherent light scattering on nanofluids was written, tested, and used to calculate the far-field intensity variation for nanofluids having different particle size. The results are discussed and an alternative experimental method for fast nanoparticle size assessing is suggested as a possible application.
Light self-confinement via second harmonic generation in a 2D nonlinear photonic crystal waveguide
2007
Spatial solitary waves induced by quadratic nonlinearities have been the subject of many theoretical and experimental investigations in the last decade, with extensive studies being devoted to soliton formation in 1D nonlinear photonic crystals (NPC) such as PPLN (periodically poled LiNbO3). Here we present results on a new class of (1 + 1)D spatial solitary waves, the first examples of quadratic self-confinement in a 2D NPC.
Four-wave mixing instabilities in telecom fibers
2012
Instabilities in fiber four-wave mixing are investigated, revealing the formation of colliding dispersive shock waves in the normal GVD regime and collective modulation instabilities in the anomalous GVD regime.
Stationary and Pulsating Dissipative Optical Bullets
2006
We demonstrate the existence of stable optical light bullets in nonlinear dissipative media. Beyond the domain where stable bullets are found, unstable bullets show unusual behaviors, like "optical rockets", pulsating solutions or pattern formation.