Boundary problems for the Ginzburg-Landau equation
نویسنده
چکیده
We provide a study at the boundary for a class of equation including the Ginzburg-Landau equation as well as the equation of travelling waves for the Gross-Pitaevskii model. We prove Clearing-Out results and an orthogonal anchoring condition of the vortex on the boundary for the Ginzburg-Landau equation with magnetic field.
منابع مشابه
Exact solutions of the 2D Ginzburg-Landau equation by the first integral method
The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.
متن کاملSome new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...
متن کاملTwo Boundary Value Problems for the Ginzburg-landau Equation
Two boundary value problems for the Ginzburg-Landau equation are considered. Extensive numerical calculations have been performed in each case, including bifurcation histories, spectral analysis, PoincarC sections and Hausdorff dimension estimates. The approach to the inviscid limit is given detailed treatment. In this case universal behavior has been found to exist. Arguments are presented to ...
متن کاملBoundary Effects in The Complex Ginzburg-Landau Equation
The effect of a finite geometry on the two-dimensional complex Ginzburg-Landau equation is addressed. Boundary effects induce the formation of novel states. For example target like-solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.
متن کاملInitial Boundary Value Problem for Generalized 2d Complex Ginzburg–landau Equation*
In this paper we study an initial boundary value problem for a generalized complex Ginzburg–Landau equation with two spatial variables (2D). Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.
متن کامل