TY - JOUR
T1 - Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation
AU - Segata, Jun Ichi
PY - 2010/7
Y1 - 2010/7
N2 - We consider the fourth order nonlinear Schrödinger 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 H8(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).
AB - We consider the fourth order nonlinear Schrödinger 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 H8(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).
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U2 - 10.3934/dcds.2010.27.1093
DO - 10.3934/dcds.2010.27.1093
M3 - Article
AN - SCOPUS:77954320757
SN - 1078-0947
VL - 27
SP - 1093
EP - 1105
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 3
ER -