耦合复金兹堡-朗道（Ginzburg-Landau）方程中的模螺旋波

摘要

以双层耦合复金兹堡-朗道（Gjnzburg-Landau）方程系统为时空模型,研究了其中的模螺旋波,讨论了这种特殊波动现象的稳定条件和相关影响因素.模螺旋波与该类时空系统中常见的相螺旋波相比,其中心不存在缺陷点,同时仅在其变量的振幅部分（而非相位部分）表现为螺旋结构.本文通过数值方法研究了耦合复金兹堡-朗道方程中产生模螺旋波所需要的初始和参数条件.研究表明,当双层耦合系统的初始斑图之间的差距较大时,才能够产生模螺旋波;同时观察到系统在参数不匹配的条件下会发生相螺旋波向模螺旋波的转变.通过对同步函数的计算,发现该转变过程具有非连续性.%A novel amplitude spiral wave in coupled complex Ginzburg-Landau equation （CGLE） system is proposed. The stability conditions and the relevant factors are investigated via numerical simulations. On the tip of an amplitude spiral wave there exist no topological defect, which is different from the commonly observed phase spiral wave, and in its amplitude part （instead of phase part） there is a spiral structure. In this research, the stability of amplitude spiral wave is studied by considering the different initial patterns in the case of the system parameter mismatches.