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Pattern Formation and Solitons papers — page 2

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Wave Number of Maximal Growth in Viscous Magnetic Fluids of Arbitrary Depth
An analytical method within the frame of linear stability theory is presented for the normal field instability in magnetic fluids. It allows to calculate the maximal growth rate and the corresponding…
Adrian Lange, Bert Reimann, Reinhard RichterSep 21, 1999
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Influence of four-wave mixing and walk-off on the self-focusing of coupled waves
Four-wave mixing and walk-off between two optical beams are investigated for fo cusing Kerr media. It is shown that four-wave mixing reinforces the self-focusi ng of mutually-trapped waves by…
L. Berge, O. Bang, W. KrolikowskiSep 13, 1999
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Multi-Bunch Solutions of Differential-Difference Equation for Traffic Flow
Newell-Whitham type car-following model with hyperbolic tangent optimal velocity function in a one-lane circuit has a finite set of the exact solutions for steady traveling wave, which expressed by…
Ken NakanishiSep 5, 1999
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Diffusion-induced vortex filament instability in 3-dimensional excitable media
We studied the stability of linear vortex filaments in 3-dimensional (3D) excitable media, using both analytical and numerical methods. We found an intrinsic 3D instability of vortex filaments that…
Zhilin Qu, Fagen Xie, Alan GarfinkelSep 1, 1999
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Dissipation in ferrofluids: Mesoscopic versus hydrodynamic theory
Part of the field dependent dissipation in ferrofluids occurs due to the rotational motion of the ferromagnetic grains relative to the viscous flow of the carrier fluid. The classical theoretical…
Hanns Walter Müller, Andreas EngelSep 1, 1999
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Long-Lived Localized Field Configurations in Small Lattices: Application to Oscillons
Long-lived localized field configurations such as breathers, oscillons, or more complex objects naturally arise in the context of a wide range of nonlinear models in different numbers of spatial…
Marcelo Gleiser, Andrew SornborgerAug 29, 1999
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Approximate solutions and scaling transformations for quadratic solitons
We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate,…
Andrey A. SukhorukovAug 29, 1999
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Stability of multi-parameter solitons: Asymptotic approach
General asymptotic approach to the stability problem of multi-parameter solitons in Hamiltonian systems i∂ En/∂ z=δH/δEn* has been developed. It has been shown that asymptotic…
Dmitry V. SkryabinAug 19, 1999
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Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems
Numerical simulations of two dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong…
Markus Baer, Aric Hagberg, Ehud Meron et al.Aug 16, 1999
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Universal Algebraic Relaxation of Velocity and Phase in Pulled Fronts generating Periodic or Chaotic States
We investigate the asymptotic relaxation of so-called pulled fronts propagating into an unstable state. The ``leading edge representation'' of the equation of motion reveals the universal…
Cornelis Storm, Willem Spruijt, Ute Ebert et al.Aug 16, 1999
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Renormalization study of two-dimensional convergent solutions of the porous medium equation
In the focusing problem we study a solution of the porous medium equation ut=Δ(um) whose initial distribution is positive in the exterior of a closed non-circular two dimensional region, and zero…
S. I. Betelu, D. G. Aronson, S. B. AngenentAug 11, 1999
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Longwave Interface Instability In Two-Fluid Vibrational Flow
We consider longwave mode of the interface instability in the system comprising of two immiscible fluid layers. The fluids fill out plane horizontal cavity which is subjected to horizontal harmonic…
Mikhail V. Khenner, Dmitrii V. LyubimovAug 11, 1999
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Bilateral symmetry breaking in a nonlinear Fabry-Perot cavity exhibiting optical tristability
We show the existence of a region in the parameter space that defines the field dynamics in a Fabry-Perot cylindrical cavity, where three output stable stationary states of the light are possible for…
Juan P. Torres, Jack Boyce, Raymond Y. ChiaoAug 6, 1999
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Crystallization Kinetics in the Swift--Hohenberg Model
It is shown numerically and analytically that the front propagation process in the framework of the Swift-Hohenberg model is determined by periodic nucleation events triggered by the explosive growth…
Igor S. Aranson, Boris A. Malomed, Len M. Pismen et al.Aug 5, 1999
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Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows.…
Yuji Igarashi, Katsumi Itoh, Ken Nakanishi et al.Aug 5, 1999
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Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators
We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to…
R. Gallego, M. San Miguel, R. ToralJul 30, 1999
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Instabilities and Spatio-Temporal Chaos in Hexagon Patterns with Rotation
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with…
Filip Sain, Hermann RieckeJul 27, 1999
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Quasiperiodic Envelope Solitons
We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the…
Carl Balslev Clausen, Yuri S. Kivshar, Ole Bang et al.Jul 26, 1999
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Dynamics of localized structures in vector waves
Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is…
Emilio Hernandez-Garcia, Miguel Hoyuelos, Pere Colet et al.Jul 16, 1999
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Curvature-induced symmetry breaking in nonlinear Schrodinger models
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically…
Yu. B. Gaididei, S. F. Mingaleev, P. L. ChristiansenJul 14, 1999
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Two-color nonlinear localized photonic modes
We analyze second-harmonic generation (SHG) at a thin effectively quadratic nonlinear interface between two linear optical media. We predict multistability of SHG for both plane and localized waves,…
Andrey A. Sukhorukov, Yuri S. Kivshar, Ole BangJul 10, 1999
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Electric Nusselt number characterization of electroconvection in nematic liquid crystals
We develop a characterization method of electroconvection structures in a planar nematic liquid crystal layer by a study of the electric current transport. Because the applied potential difference…
J. T. Gleeson, N. Gheorghiu, E. PlautJul 8, 1999
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Modelling the dynamics of turbulent floods
Consider the dynamics of turbulent flow in rivers, estuaries and floods. Based on the widely used k-epsilon model for turbulence, we use the techniques of centre manifold theory to derive dynamical…
Z. Mei, A. J. Roberts, Zhenquan LiJun 25, 1999
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Dispersion relations to oscillatory reaction-diffusion systems with the self-consistent flow
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and…
Hiroyasu Yamada, Toshiyuki NakagakiJun 24, 1999
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Soliton Interactions in Perturbed Nonlinear Schroedinger Equations
We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the…
James A. Besley, Peter D. Miller, Nail N. AkhmedievJun 9, 1999
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