Long time behavior and singular limit for solution tononlinear dispersive equation

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We considered the long time behavior of solutions to nonlinear dispersive partial differential equations arises in various fields of physics and engineering. Especially, we focused on solvability, scattering problem, and the stability of some special solutions called standing waves for the higher order nonlinear Schrodinger type equation arising in context of the motion of vortex filament. We also studied the semiclassical limit of Schrodinger-KdV system which describes an interaction betweenlong and short waves.