The inviscid limit of the derivative complex Ginzburg–Landau equation

AbstractWe show that the solutions of the derivative complex Ginzburg–Landau equation ut−(ε+i)uxx+(a+i)g(|u|2)u+(α+iβ)(|u|2u)x=0 converge to the solution of the derivative nonlinear Schrödinger equation ut−iuxx+ig(|u|2)u+α(|u|2u)x=0 if the real parameters ε, a and β tend to 0. Moreover, an optimal convergence rate is also given