各向异性复Ginzburg-Landau方程的相扩散方程
Phase-Diffusion Equations for the Anisotropic Complex Ginzburg-Landau Equation
摘要：
各向异性复Ginzburg-Landau方程（ACGLE）描述了在各向异性空间扩展系统中具有零波数的振荡（Hopf）不稳定性附近的图案的慢调制。ACGLE的行波解在Benjamin-Feir-Newell不稳定性附近变得不稳定。我们确定了两个不稳定的条件，在参数空间和研究余维一（-两）分岔发生，如果一（两）的条件是（是）满足。我们推导出各向异性Kuramoto-Sivashinsky型方程，该方程控制ACGLE的复解的相位，并从相位方程的解生成ACGLE的解。
英文摘要：
The anisotropic complex Ginzburg-Landau equation (ACGLE) describes slow modulations of patterns in anisotropic spatially extended systems near oscillatory (Hopf) instabilities with zero wavenumbers. Traveling wave solutions to the ACGLE become unstable near Benjamin-Feir-Newell instabilities. We determine two instability conditions in parameter space and study codimension-one (-two) bifurcations that occur if one (two) of the conditions is (are) met. We derive anisotropic Kuramoto-Sivashinsky-type equations that govern the phase of the complex solutions to the ACGLE and generate solutions to the ACGLE from solutions of the phase equations.
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