Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation

The modified complex Ginzburg-Landau equation (mCGLE) which includes a dela yed response term in the integral form is analysed. In particular, a singul arity analysis of mCGLE is presented. It is shown that this equation fails to pass the Painleve test when the non-conservative terms are nonzero. Neve rtheless, exact solutions to this equation do exist. Stationary solutions c an be treated using the 'segment balance' method which is an extension of c onservation laws to non-conservative systems. This method is used to derive an exact soliton solution of mCGLE.