Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Abstract

In this paper, we investigate the one-dimensional derivative nonlinear Schrödinger equations of the form $iu_t-u_{xx}+iλ\abs{u}^k u_x=0$ with non-zero $λ\in \Real$ and any real number $k\gs 5$. We establish the local well-posedness of the Cauchy problem with any initial data in $H^{1/2}$ by using the gauge transformation and the Littlewood-Paley decomposition.

25 pages

References in corpus (1)

• On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations