Takaoka, Hideo Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity. (English) Zbl 0951.35125 Adv. Differ. Equ. 4, No. 4, 561-580 (1999). It is shown that the Cauchy problem for a certain class of one-dimensional nonlinear Schrödinger equations involving a derivative in the nonlinearity is well-posed in the space \(H^1_2\). The proof is based on the Fourier restriction norm and gauge transformation. After an introduction which states the problem and displays the main result, the author derives various preliminary estimates, and proves then his main result, which is an improvement of known results. Reviewer: Guy Jumarie (Montréal) Cited in 2 ReviewsCited in 63 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:Cauchy problem; nonlinear Schrödinger equations; derivative in the nonlinearity PDFBibTeX XMLCite \textit{H. Takaoka}, Adv. Differ. Equ. 4, No. 4, 561--580 (1999; Zbl 0951.35125)