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Bibliography

1
J. Barab: Nonexistence of asymptotically free solutions for a nonlinear Schrödinger equation, J. Math. Phys. 25 (1984), 3270-3273.

2
J. Bergh and J. Löfström: Interpolation spaces, An introduction, Springer Verlag, 1976.

3
T. Cazenave and F. B. Weissler: The Cauchy problem for nonlinear Schrödinger equation in $ H^s$, Nonlinear Anal. 14 (1990), 807-836.

4
T. Cazenave and F. B. Weissler: Rapidly decaying solutions of the nonlinear Schrödinger equation, Comm. Math. Phys. 147 (1992), 75-100.

5
J. Ginibre and T. Ozawa: Long range scattering for nonlinear Schrödinger and Hartree equations in space dimension $ n \ge 2$, Comm. Math. Phys. 151 (1993), 619-645.

6
J. Ginibre, T. Ozawa and G. Velo: On the existence of the wave operators for a class of nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 60 (1994), 211-239.

7
J. Ginibre and G. Velo: On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case, J. Funct. Anal. 32 (1979), 1-32.

8
J. Ginibre and G. Velo: On a class of nonlinear Schrödinger equations. II. Scattering theory, general case, J. Funct. Anal. 32 (1979), 33-71.

9
J. Ginibre and G. Velo: Scattering theory in the energy space for a class of nonlinear Schrödinger equations, J. Math. Pures Appl. 64 (1985), 363-401.

10
J. Ginibre and G. Velo: The global Cauchy problem for the nonlinear Klein-Gordon equation, Math. Z. 189 (1985), 487-505.

11
N. Hayashi and P. I. Naumkin: Asymptotic behavior in time of solutions to the nonlinear Schrödinger and Hartree equations, Amer. J. Math. 120 (1998), 369-389.

12
N. Hayashi and Y. Tsutsumi: Scattering theory for Hartree type equations, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987), 187-213.

13
T. Kato: On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987), 113-129.

14
T. Kato: On nonlinear Schrödinger equations, II. $ H^s$ solutions and unconditional well-posedness, J. Anal. Math. 67 (1995), 281-306.

15
N. Kita: Sharp $ L^r$ asymptotics of the solutions to nonlinear Schrödinger equations, preprint.

16
J. E. Lin and W. A. Strauss: Decay and scattering of solutions of a nonlinear Schröinger equation, J. Funct. Anal. 30 (1978), 245-263.

17
M. Nakamura and T. Ozawa: Low energy scattering for nonlinear Schrödinger equations in fractional order Sobolev spaces, Rev. Math. Phys. 9 (1997), 397-410.

18
K. Nakanishi: Energy scattering for nonlinear Klein-Gordon and Schrödinger equations in spatial dimensions $ 1$ and $ 2$, J. Funct. Anal. 169 (1999), 201-225.

19
T. Ozawa: Long range scattering for nonlinear Schrödinger equations in one space dimension, Comm. Math. Phys. 139 (1991), 479-493.

20
W. A. Strauss: Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981), 110-133.

21
Y. Tsutsumi: Scattering problem for nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 43 (1985), 321-347.

22
Y. Tsutsumi: $ L^2$-solutions for nonlinear Schrödinger equations and nonlinear groups, Funkcial. Ekvac. 30 (1987), 115-125.

23
Y. Tsutsumi and K. Yajima: The asymptotic behavior of nonlinear Schrödinger equations, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 186-188.

24
T. Wada: Asymptotic expansion of the solution to the nonlinear Schrödinger equation with nonlocal interaction, to appear in J. Funct. Anal.



Naoyasu Kita
Graduate School of Mathematics
Kyushu University
Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan
E-mail: nkita@moon.ap.kyushu-u.ac.jp


Takeshi Wada
Department of Mathematics
Graduate School of Science, Osaka University
Toyonaka, Osaka 560-0043, Japan
E-mail: wada@math.sci.osaka-u.ac.jp



Nobuki Takayama 2002-04-24