Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament. (English) Zbl 1042.35077

Segata, J.

Differ. Integral Equ. 16, No. 7, 841-864 (2003).

The author studies the initial value problem for a 1D nonlinear Schrödinger-type equation with variable coefficients. He proves time-local well-posedness in the Sololev space \(H^s(\mathbb{R})\) for \(0.5\leq s\).

Reviewer: Igor Andrianov (Köln)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
76D17	Viscous vortex flows
35B30	Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs

Keywords:

nonlinear Schrödinger-type equation; initial value problem; time-local well-posedness