Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Details Well-posedness for one-dimensional derivative nonlinear Schrödinger equations Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

2008-11-26

arxiv.org/abs/0811.4222v1

Comm. Pure Appl. Anal., 6(4), 997-1021, 2007

Mathematics

Analysis of PDEs

25 pages

Scientific paper

In this paper, we investigate the one-dimensional derivative nonlinear
Schr\"odinger equations of the form $iu_t-u_{xx}+i\lambda\abs{u}^k u_x=0$ with
non-zero $\lambda\in \Real$ 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.

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