Skip to content

Pattern Formation and Solitons papers — page 17

patt-solBrowse archive

Domain Structures in Fourth-Order Phase and Ginzburg-Landau Equations
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For…
David Raitt, Hermann RieckeFeb 18, 1994
Learn
SUSY-Based Variational Method for the Anharmonic Oscillator
Using a newly suggested algorithm of Gozzi, Reuter, and Thacker for calculating the excited states of one dimensional systems, we determine approximately the eigenvalues and eigenfunctions of the…
Fred Cooper, John Dawson, Harvey ShepardFeb 17, 1994
Learn
Structure And Dynamics Of Modulated Traveling Waves In Cellular Flames
We describe spatial and temporal patterns in cylindrical premixed flames in the cellular regime, Le < 1, where the Lewis number Le is the ratio of thermal to mass diffusivity of a deficient…
A. Bayliss, B. J. Matkowsky, H. RieckeFeb 4, 1994
Learn
Front Structures in a Real Ginzburg-Landau Equation Coupled to a Mean Field
Localized traveling wave trains or pulses have been observed in various experiments in binary mixture convection. For strongly negative separation ratio, these pulse structures can be described as…
Henar Herrero, Hermann RieckeJan 28, 1994
Learn
Kink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and…
Angel Sanchez, A R Bishop, Francisco Dominguez-AdameJan 24, 1994
Learn
Domain Structures and Zig-Zag Patterns Modeled by a Fourth-Order Ginzburg-Landau Equation
Domain walls between spatially periodic patterns with different wave numbers, can arise in pattern-forming systems with a neutral curve that has a double minimum. Within the framework of the phase…
David Raitt, Hermann RieckeJan 24, 1994
Learn
Soliton solutions of the Hamiltonian DSI and DSIII equations
By introducing generalized Backlund Transformations depending on arbitrary functions, wave and localized soliton solutions of the Davey- Stewartson equations are generated. Moreover explicit soliton…
Flora PempinelliJan 10, 1994
Learn
From Labyrinthine Patterns to Spiral Turbulence
A new mechanism for spiral vortex nucleation in nongradient reaction diffusion systems is proposed. It involves two key ingredients: An Ising-Bloch type front bifurcation and an instability of a…
Aric Hagberg, Ehud MeronJan 5, 1994
Learn
Hydrothermal Surface-Wave Instability and the Kuramoto-Sivashinsky Equation
We consider a system formed by an infinite viscous liquid layer with a constant horizontal temperature gradient, and a basic nonlinear bulk velocity profile. In the limit of long-wavelength and large…
R. A. Kraenkel, J. G. Pereira, M. A. MannaJan 4, 1994
Learn
Multiple Front Propagation into Unstable States
The dynamics of transient patterns formed by front propagation in extended nonequilibrium systems is considered. Under certain circumstances, the state left behind a front propagating into an…
R. Montagne, A. Amengual, E. Hernandez-Garcia et al.Dec 10, 1993
Learn
Dual Fronts Propagating into an Unstable State
The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an…
F. J. Elmer, J. -P. Eckmann, G. HartslebenNov 26, 1993
Learn
Solitons in the Camassa-Holm Shallow Water Equation
We study the class of shallow water equations of Camassa and Holm derived from the Lagrangian: $ L= ∫ ( 12 (φxxx-φx )φt - 1 2 (φx)3 - 1 …
Fred Cooper, Harvey ShepardNov 22, 1993
Learn
Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves
A two dimensional model is introduced to study pattern formation, secondary instabilities and the transition to spatiotemporal chaos (weak turbulence) in parametric surface waves. The stability of a…
Wenbin Zhang, Jorge VinalsNov 19, 1993
Learn
D4+ T2 Mode Interactions and Hidden Rotational Symmetry
Bifurcation problems in which periodic boundary conditions or Neumann boundary conditions are imposed often involve partial differential equations that have Euclidean symmetry. As a result the normal…
John David CrawfordNov 14, 1993
Learn
Properties Of Solutions Of The Kpi Equation
The Kadomtsev--Petviashvili I (KPI) is considered as a useful laboratory for experimenting new theoretical tools able to handle the specific features of integrable models in 2+1 dimensions. The…
M. Boiti, F. FempinelliNov 12, 1993
Learn
Multidimensional Localized Solitons
Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions.…
M. Boiti, L. Martina, F. PempinelliNov 12, 1993
Learn
Oscillatory instability of crack propagations in quasi-static fracture
Crack propagations in quasi-static fracture are studied theoretically. The Griffith theory is applied to discuss a crack extension condition and motion of crack tips in straight propagations.…
Shin-ichi Sasa, Ken SekimotoNov 5, 1993
Learn
On the existence of monotonic fronts for a class of physical problems described by the equation λu''' + u' = f(u)
We obtain an upper bound on the value of λ for which monotonic front solutions of the equation λu''' + u' = f(u) with λ> 0 may exist.
R. D. Benguria, M. C. DepassierNov 4, 1993
Learn
D4-symmetric Maps with Hidden Euclidean Symmetry
Bifurcation problems in which periodic boundary conditions (PBC) or Neumann boundary conditions (NBC) are imposed often involve partial differential equations that have Euclidean symmetry. In this…
John David CrawfordNov 2, 1993
Learn
Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
We analyze the nonlinear dynamics near the incoherent state in a mean-field model of coupled oscillators. The population is described by a Fokker-Planck equation for the distribution of phases, and…
John David CrawfordOct 28, 1993
Learn
Exact Solutions of the One-Dimensional Quintic Complex Ginzburg-Landau Equation
Exact solitary wave solutions of the one-dimensional quintic complex Ginzburg-Landau equation are obtained using a method derived from the Painlevé test for integrability. These solutions are…
Philippe Marcq, Hugues Chate', Robert ConteOct 22, 1993
Learn
Temporal Forcing of Small-Amplitude Waves in Anisotropic Systems
We investigate the effect of resonant temporal forcing on an anisotropic system that exhibits a Hopf bifurcation to obliquely traveling waves in the absence of this forcing. We find that the forcing…
Hermann Riecke, Mary Silber, Lorenz KramerOct 15, 1993
Learn
Thermodynamic Limit Of The Ginzburg-Landau Equations
We investigate the existence of a global semiflow for the complex Ginzburg-Landau equation on the space of bounded functions in unbounded domain. This semiflow is proven to exist in dimension 1 and 2…
P. ColletOct 14, 1993
Learn
Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed…
Hugues Chate'Oct 12, 1993
Learn
Nonradial Solutions of a Semilinear Elliptic Equation in Two Dimensions
: We establish existence of an infinite family of exponentially-decaying non-radial C2 solutions to the equation Δu + f(u) = 0 on R2 for a large class of nonlinearities f. These solutions…
Joseph Iaia, Henry WarchallSep 13, 1993
Learn
← PreviousPage 17Next →