Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity
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.
scientific article; zbMATH DE number 1493601