WELL-POSEDNESS AND EXISTENCE OF STANDING WAVES FOR THE FOURTH ORDER NONLINEAR SCHRODINGER TYPE EQUATION

We consider the fourth order nonlinear Schrodinger type equation (4NLS). The first purpose is to revisit the well-posedness theory of (4NLS). In [8], [9], [20] and [21], they proved the time-local well-posedness of (4NLS) in H-s(R) with s > 1/2 by using the Fourier restriction method. In this paper we give another proof of above result by using simpler approach than the Fourier restriction method. The second purpose is to construct the exact standing wave solution to (4NLS).