MR2297946
Hayashi, Nakao and Naumkin, Pavel I.
Nakao HAYASHI and Pavel I. NAUMKIN
Asymptotics in Time of Solutions to Nonlinear Schrödinger Equations in Two Space Dimensions
Funkcialaj Ekvacioj. Serio Internacia
49
2006
415--425
http://fe.math.kobe-u.ac.jp/FE/FullPapers/49-3/49_415.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2297946
We study asymptotics of solutions around the final states of nonlinear Schrödinger equations with quadratic nonlinearities in two space dimensions.
Nonlinear Schrödinger equations, Quadratic nonlinearity, Two space dimensions.
35Q35.
49-415
2006
Asymptotics in Time of Solutions to Nonlinear Schrödinger Equations in Two Space Dimensions
HAYASHI, Nakao and NAUMKIN, Pavel I.
Nakao HAYASHI and Pavel I. NAUMKIN
1
Hayashi, N.; Kawahara, Y.; Naumkin, P. I., Lower bounds of asymptotics in time of solutions to Nonlinear Schrödinger Equations in 3d, to appear in Cubo. A. Math. J.
2
Hayashi, N.; Naumkin, P. I.; Shimomura, A.; Tonegawa, S.
Modified wave operators for nonlinear Schrödinger equations in one and two dimensions
Electron. J. Differential Equations
62
2004
1-16
MR2047418
3
Kita, N.
Sharp $L^r$ asymptotics of the small solutions to the nonlinear Schrödinger equations
Nonlinear Anal.
52
2003
1365-1377
MR1941262
4
Kita, N.; Ozawa, T.
Sharp asymptotic behavior of solutions to nonlinear Schrödinger equations with repulsive interactions
Commun. Contemp. Math.
7
2005
167-176
MR2140548
5
Kita, N.; Wada, T.
Sharp asymptotic behavior of solutions to nonlinear Schrödinger equations in one space dimension
Funkcial. Ekvac.
45
2002
53-69
MR1913680
1913680
6
Kita, N.; Wada, T.
Sharp asymptotics of the small solutions to the nonlinear Schrödinger equations of derivative type
Differential Integral Equations
15
2002
367-384
MR1870648
7
Moriyama, K.; Tonegawa, S.; Tsutsumi, Y.
Wave operators for the nonlinear Schrödinger equation with a nonlinearity of low degree in one or two dimensions
Commun. Contemp. Math.
5
2003
983-996
MR2030566
8
Nakanishi, K.; Ozawa, T.
Remarks on scattering for nonlinear Schrödinger equations
NoDEA Nonlinear Differential Equations Appl.
9
2002
45-68
MR1891695
9
Shimomura, A.
Non-existence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in two space dimensions
Differential Integral Equations
18
2005
325-335
MR2122723
10
Shimomura, A.; Tonegawa, S.
Long range scattering for nonlinear Schrödinger equations in one and two space dimensions
Differential Integral Equations
17
2004
127-150
MR2035499
11
Wada, T.
Asymptotic expansion of the solution to the nonlinear Schrödinger equation with nonlocal interaction
J. Funct. Anal.
180
2001
11-30
MR1814421