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We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrödinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators… (More)

We consider the initial value problem for some nonlinear hyperbolic and dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system.

- Jun-Ichi Segata
- 2010

We consider the initial value problem for the fourth-order non-linear Schrödinger-type equation (4NLS) which describes the motion of an isolated vortex filament. In the first part of this note we review some recent results on the time local well-posedness of (4NLS) and give the alternative proof of those results. In the second part of this note we consider… (More)

We consider the behavior of solutions to the water wave interaction equations in the limit ε → 0+. To justify the semiclassical approximation, we reduce the water wave interaction equation into some hyperbolic-dispersive system by using a modified Madelung transform. The reduced system causes loss of derivatives which prevents us to apply the classical… (More)

- Jun-Ichi Segata
- Asymptotic Analysis
- 2011

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