時空間変調下での散逸ソリトンのダイナミクス (非線形波動現象の数理とその応用)

Abstract

The complex Ginzburg-Landau equation (CGLE) is a general model of spatially extended nonequilibnum systems. In this paper, an analytical method for solving a variable coefficient CGLE (VCCGLE) is presented to obtain exact solutions. Variable transformations for space and time variables with coefficient functions yield an imaginary time advection equation related to a complex valued characteristic curve. The VCCGLE is transformed into the nonlinear Schrodinger equation (NLSE) on the complex valued characteristic curve. This result indicates that the exact solutions of the NLSE generate that of the VCCGLE. Examples of the exact solutions of the VCGLE are presented through those of the NLSE.