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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
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