Inviscid limit behavior of the solution to the one-dimensional generalized Ginzburg–Landau equation

The Cauchy problem for the one-dimensional generalized Ginzburg–Landau (GGL) equation is considered and the inviscid limit behavior of its solution is proved. That is, the solution of Cauchy problem for the GGL equation converges to the solution of Cauchy problem for the derivative nonlinear Schrödinger equation in the natural space C([0,T];Hs)C([0,T];Hs) with s>12, for some T>0T>0, if some coefficients tend to zero. Moreover, the convergence holds in C([0,T];H1)C([0,T];H1) for any T>0T>0 if initial data belong to H2H2. Furthermore, the convergence also holds in C([0,T];Hs)C([0,T];Hs) for any T>0T>0 if initial data belong to Hs(s>47) with some coefficients conditions.