Mathematics – Analysis of PDEs
Scientific paper
2008-11-26
J. Math. Anal. Appl., 328(1), 58-83, 2007
Mathematics
Analysis of PDEs
28 pages
Scientific paper
10.1016/j.jmaa.2006.05.031
We study the wellposedness of Cauchy problem for the fourth order nonlinear Schr\"odinger equations i\partial_t u=-\eps\Delta u+\Delta^2 u+P((\partial_x^\alpha u)_{\abs{\alpha}\ls 2}, (\partial_x^\alpha \bar{u})_{\abs{\alpha}\ls 2}),\quad t\in \Real, x\in\Real^n, where $\eps\in\{-1,0,1\}$, $n\gs 2$ denotes the spatial dimension and $P(\cdot)$ is a polynomial excluding constant and linear terms.
Hao Chengchun
Hsiao Ling
Wang Baoxiang
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