The inviscid limit of the derivative complex Ginzburg-Landau equation

We show that the solutions of the derivative complex Ginzburg-Landau equation: ut-(ε+i)*uxx + (a+i)*g(|u|2)*u + (α+i*β)*(|u|2*u)x 0 converge to the solution of the derivative nonlinear Schroedinger equation ut-i*uxx + i*g(|u|2)*u+α(|u|2*u)x = 0 if the real parameters ε, α, and β tend to 0. Moreover, an optimal convergence rate is also given. (authors)