The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line. (English) Zbl 1212.35448

Holmer, Justin

Differ. Integral Equ. 18, No. 6, 647-668 (2005).

Summary: By adapting the method of J.E.Colliander and C.E.Kenig [Commun.Partial Differ.Equations 27, No. 11-12, 2187–2266 (2002; Zbl 1041.35064)], local well posedness of the initial-boundary-value problem for the one-dimensional nonlinear Schrödinger equation \(\text{i}\partial _tu+\partial ^2_xu+\lambda u| u| ^{\alpha -1}=0\) is proved. The equation is considered on the half-line under low boundary regularity assumptions.

MSC:

35Q55

NLS equations (nonlinear Schrödinger equations)

Keywords:

well posedness

Citations:

Zbl 1041.35064