The inviscid limit of the derivative complex Ginzburg–Landau equation

摘要

We show that the solutions of the derivative complex Ginzburg–Landau equation u_t-(ε+ i) * u_(xx) + (a + i)g(|u|~2) u + (α + iβ)(|u|~2u) x = 0 converge to the solution of the derivative nonlinear Schrodinger equation u_t-iu_(xx) + ig(|u|~2)u + α(|u|~2u)_x = 0 if the real parameters ε, α, and β tend to 0. Moreover, an optimal convergence rate is also given.