03 Keith Promislow and Roger Temam Approximate Interaction Laws for Small and Large Waves in the Ginzburg-Landau Equation IMA J. Arjen Doelman Slow time-periodic solutions of the Ginzburg-Landau equation Phys.


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Geometric Theory Bifurcations and Splitting Dynamics.

Arjen doelman slow time-periodic solutions of the ginzburg-landauequation. A relative periodic solution is a solution that is periodic in time up to a. The spatial quasiperiodic solutions disappear due to the perturbation are proved. Arjen Doelman Finite-dimensional models of the Ginzburg-Landau equation Nonlinearity 4 1991 no.

Kaper 2006 A geometric construction of traveling waves in a bioremediation model J. Last time updated on 652019 View original full text link. This paper was published in Crossref.

Arjen Doelman Bjorn Sandstede Arnd Scheel Guido Schneider. 16 4 329 - 349. Z t is a solution of 14 of the form z t p z eBz-ewrl 15 w plays the role of a free parameter.

In this paper we study slow time periodic solutions of the Ginzburg-Landau equation with small complex coefficients ie. This system is perturbed by considering modulation equations. Van der Ploeg A.

A Note on the analytic solutions of the CamassaHolm equation. Doelman Arjen Abstract In this paper we study the behaviour of solutions of the form ψ z t φ z e -iwt 1 of the rescaled Ginzburg-Landau equation ψ t 1 - 1 i B ψ 2 ψ 1 i A ψ zz for A a B b w plays the role of free parameter. We show that the solutions of the Ginzburg-Landau equation on a periodic interval are of Gevrey-class regularity.

The complex cubic GinzburgLandau equation 19 31. ARJEN DOELMAN TASSO J. Author links open overlay panel Arjen Doelman.

TMA 16 1991 959-980. In this paper we study the behaviour of solutions of the form ψz t φz e iϵwt ϵ 1 of the rescaled Ginzburg-Landau equation. Abstract Abstract is not available.

In this paper the Ginzburg-Landau equation with small complex coefficients is considered. Using this preliminary result we establish that the N-dimensional linear Galerkin approximation of u converges exponentially fast to uas N goes to infinity. A translation is introduced to transform the Ginzburg-Landau equation into a dynamical system.

Slow time-periodic solutions of the Ginzburg-Landau equation. First we determine the stability of periodic solutions. A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation CGLE with periodic boundary conditions.

The generalized Gierer-Meinhardt equation is a paradigm model of two coupled reaction-diffusion equations in the theory of biological pattern formation. 54 5 1219 - 1301. Doelman 2005 Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations Indiana Univ.

Are the locally preferred planform for the complex Ginzburg-Landau equation - -10 In order to describe the spatial global behavior an evolution equation for the local wave number 2 can be derived formally. We construct stable waves that are time-periodic in an appropriately moving coordinate frame and whose profile converges as. Inspired on similar phenomena appearing in the analysis of so-called localized structures in modulation or amplitude equations we consider a family of nearly integrable singularly perturbed three dimensional vector fields with two bifurcation parameters a and b.

Specifically we prove that the modes of the Fourier decomposition of a solution u decay exponentially. Slow time-periodic solutions of the Ginzburg-Landau equation. A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg--Landau equation CGLE with periodic boundary conditions.

SLOW TIME-PERIODIC SOLUTIONS OF THE GINZBURG-LANDAU EQUATION Arjen DOELMAN Mathematisch lnstituut Rijksuniversiteit Utrecht Postbus 80010 3508 TA Utrecht The Netherlands Received 1 April 1989 Revised manuscript received 18 July 1989 Accepted 20 July 1989 Communicated by H. 2001 Slowly Modulated Two-Pulse Solutions in the Gray--Scott Model II. KAPERt AND HARMEN VAN DER PLOEG Abstract.

On the Lp regularity of solutions to the generalized Hunter-Saxton system with Jaeho Choi Nitin Krishna and Nicole Magill. Moreover the existence and the properties of the equilibria are discussed. Home Browse by Title Periodicals Physica D Vol.

There exist families of quasi-periodic and homoclinic solutions. Download Citation Spatial heteroclinic bifurcation of time periodic solutions to the GinzburgLandau equation We study the spatial structure of the. Slowly-varying modulations of the k 0 wave train.

The stationary problem is like in the non-degenerate case integrable. Crossref Provided a free PDF. A relative periodic solution is a solution that is periodic in time up to a transformation by an.

The existence of time independent spatially periodic patterns of this equation in one space dimension is governed by a. Ginzburg-Landau equation Ian Melbourne and Guido Schneider March 13 2003 Abstract For stable time periodic solutions. Up to 10 cash back In this paper we study the creation of homoclinic orbits by saddle-node bifurcations.

2 Slow time-periodic solutions of the Ginzburg-Landau equation. Sorry we are unable to provide the full text but you may find it at the following locations. D 40 1989 no.

Arjen Doelman Wiktor Eckhaus and Tasso J. Slow Time-periodic solutions of the cubic-quinitic Ginzburg-Landau equation articleGuo1996SlowTS titleSlow Time-periodic solutions of the cubic-quinitic Ginzburg-Landau equation authorBoling Guo and Zhu-jun Jing and Bainian Lu journalCommunications in Nonlinear Science and Numerical Simulation. 04 Keith Promislow Time Analyticity and Gevrey Regularity for solutions of a class of Dissipative Partial Differential Equations Nonlinear Anal.

On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations. Slow time-periodic solutions of the Ginzburg-Landau equation. Abstract PDF 347 KB.

SIAM Journal on Applied Mathematics 616 2036-2062.


Arjen Doelman Professor Leiden University Leiden Lei Mathematical Institute