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Pattern Formation and Solitons papers — page 16

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Observation of Conservations Laws in Diffusion Limited Aggregation
We repeat the numerical experiments for diffusion limited aggregation (DLA) and show that there is a potentially infinite set of conserved quantities for the long time asymptotics. We connect these…
Mark B. Mineev-Weinstein, Ronnie MainieriDec 6, 1994
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Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection
A theory of the novel spiral chaos state recently observed in Rayleigh-Benard convection is proposed in terms of the importance of invasive defects i.e defects that through their intrinsic dynamics…
M. C. Cross, Yuhai TuDec 1, 1994
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On the validity of mean-field amplitude equations for counterpropagating wavetrains
We rigorously establish the validity of the equations describing the evolution of one-dimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic model equation, namely…
R. D. Pierce, C. E. WayneNov 29, 1994
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Front propagation into unstable and metastable states in Smectic C* liquid crystals: linear and nonlinear marginal stability analysis
We discuss the front propagation in ferroelectric chiral smectics (SmC*) subjected to electric and magnetic fields applied parallel to smectic layers. The reversal of the electric field induces the…
Wim van Saarloos, Martin van Hecke, Robert HolystNov 16, 1994
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A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation
We show that the minimal speed for the existence of monotonic fronts of the equation ut = (um)xx + f(u) with f(0) = f(1) = 0, m >1 and f>0 in (0,1) derives from a variational…
R. D. Benguria, M. C. DepassierOct 27, 1994
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Bipolar Electrodiffusion model for Electroconvection in Nematics
The common description of the electrical behavior of a nematic liquid crystal as an anisotropic dielectric medium with (weak) ohmic conductivity is extended to an electrodiffusion model with two…
Martin Treiber, Lorenz KramerSep 23, 1994
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Jam phases in two-dimensional cellular automata model of traffic flow
The jam phases in a two-dimensional cellular automata model of traffic flow are investigated by computer simulations. Two different types of the jam phases are found. The spatially diagonal…
Shin-ichi Tadaki, Macoto KikuchiSep 22, 1994
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From the defocusing nonlinear Schroedinger to the complex Ginzburg-Landau equation
Perturbation approaches developed so far for the dark soliton solutions of the (fully integrable) defocusing nonlinear Schroedinger equation cannot describe the dynamics resulting from dissipative…
Olaf Stiller, Stefan Popp, Lorenz KramerSep 17, 1994
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Hole Solutions in the 1d Complex Ginzburg-Landau Equation
The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family of traveling localized source solutions. These so called 'Nozaki-Bekki holes' are (dynamically) stable in some…
Stefan Popp, Olaf Stiller, Igor Aranson et al.Sep 17, 1994
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Bound Pairs of Fronts in a Real Ginzburg-Landau Equation Coupled to a Mean Field
Motivated by the observation of localized traveling-wave states (`pulses') in convection in binary liquid mixtures, the interaction of fronts is investigated in a real Ginzburg-Landau equation…
Henar Herrero, Hermann RieckeSep 6, 1994
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Variational Characterization of the Speed of Propagation of Fronts for the Nonlinear Diffusion Equation
We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equation ut = uxx + f(u) with f(0)=f(1)=0, and f>0 in (0,1), which permits, in…
R. D. Benguria, M. C. DepassierSep 1, 1994
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Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode
An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude ρ(t) decouples from…
John David CrawfordJul 6, 1994
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The Korteweg-de Vries Hierarchy and Long Water-Waves
By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the…
R. A. Kraenkel, M. A. Manna, J. G. PereiraJun 17, 1994
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Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of…
Aric Hagberg, Ehud MeronMay 26, 1994
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New Sets of Kink Bearing Hamiltonians
Given a kink bearing Hamiltonian, Isospectral Hamiltonian approach is used in generating new sets of Hamiltonains which also admit kink solutions. We use Sine-Gordon model as a example and explicitly…
B. Dey, C. N. KumarApr 28, 1994
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Normal Form, Symmetry and Infinite Dimensional Lie Algebra for System of Ode's
The normal form for a system of ode's is constructed from its polynomial symmetries of the linear part of the system, which is assumed to be semi-simple. The symmetries are shown to have a simple…
Yuji KodamaApr 27, 1994
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Dynamic Front Transitions and Spiral-Vortex Nucleation
This is a study of front dynamics in reaction diffusion systems near Nonequilibrium Ising-Bloch bifurcations. We find that the relation between front velocity and perturbative factors, such as…
Christian Elphick, Aric Hagberg, Ehud MeronApr 25, 1994
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Example of shock wave in unstaible medium: The focusing nonlinear Schrodinger equation
Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our…
Ramil' F. Bikbaev, Vadim R. KudashevApr 21, 1994
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Whitham deformations partially saturating the modulational instability in the nonlinear Schrodinger equation
In the framework of Gurevich and Pitaevskii approach [1] we construct modulated by Whitham [2] solution of nonlinear Shrodinger (NS) equation partially saturating the modulational instability. This…
Ramil' F. Bikbaev, Vadim R. KudashevApr 20, 1994
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KdV shock-like waves as invariant solutions of KdV equation symmetries
We consider the following hypothesis: some of KdV equation shock-like waves are invariant with respect to the combination of the Galilean symmetry and KdV equation higher symmetries. Also we…
Vadim R. KudashevApr 7, 1994
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Inverse ac Josephson Effect for a Fluxon in a Long Modulated Junction
We analyze motion of a fluxon in a weakly damped ac-driven long Josephson junction with a periodically modulated maximum Josephson current density. We demonstrate both analytically and numerically…
Giovanni Filatrella, Boris A. Malomed, Robert D. ParmentierMar 30, 1994
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Kinks in the Presence of Rapidly Varying Perturbations
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on…
Yuri S. Kivshar, Niels Gr\{o}nbech-Jensen, Robert D. ParmentierMar 30, 1994
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New exact fronts for the nonlinear diffusion equation with quintic nonlinearities
We consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities ut = uxx + μu (1 -u ) ( 1 +αu + βu2 +γu3). If the parameters α, β and γ obey a special…
R. D. Benguria, M. C. DepassierMar 21, 1994
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Asymptotic expansion for layer solutions of a singularly perturbed reaction-diffusion system
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions…
Xiao-Biao LinMar 18, 1994
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On the validity of the linear speed selection mechanism for fronts of the nonlinear diffusion equation
We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation ut = uxx + f(u). It has been rigorously shown by Aronson and Weinberger that for a…
R. D. Benguria, M. C. DepassierMar 8, 1994
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