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

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 $$0.5\leq s$$.

### 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