Inviscid Limits of the Complex Ginzburg–Landau Equation
نویسنده
چکیده
In the inviscid limit the generalized complex Ginzburg–Landau equation reduces to the nonlinear Schrödinger equation. This limit is proved rigorously with H 1 data in the whole space for the Cauchy problem and in the torus with periodic boundary conditions. The results are valid for nonlinearities with an arbitrary growth exponent in the defocusing case and with a subcritical or critical growth exponent at the level of L2 in the focusing case, in any spatial dimension. Furthermore, optimal convergence rates are proved. The proofs are based on estimates of the Schrödinger energy functional and on Gagliardo–Nirenberg inequalities.
منابع مشابه
Some 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 کاملExact 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 کاملرفتار سالیتونی در مدلهای ناپایدار باروکیلینیک
Here we concern ouraelves with the derivation of a system of evolution equations for slowly varying amplitude of a baroclinic wave packet. The self-induced transparency, Sine-Gordon, and nonlinear Schrodinger equations, all of which possess soliton solutions, each arise for different inviscid limits. The presence of viscosity, however, alters the form of the evolution equations and changes th...
متن کاملLocal times for solutions of the complex Ginzburg–Landau equation and the inviscid limit
We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg–Landau equation perturbed by a random force. It was proved in [KS04] that if the random force is proportional to the square root of the viscosity ν > 0, then the family of stationary measures possesses an accumulation point as ν → 0. We show that if μ is such point, then the distributions of the L nor...
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 کامل