MR3468737 Nakao HAYASHI and Pavel I. NAUMKIN Nakao HAYASHI and Pavel I. NAUMKIN Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d Funkcialaj Ekvacioj. Serio Internacia 58 2015 451--470 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-3/58_451.pdf http://www.ams.org/mathscinet-getitem?mr=MR3468737 We consider the one dimensional nonlinear Schrödinger equation $iu_{t}+u_{xx}/2=f(u)$, $x\in\mathbf{R}$, $t>0$, $u(0,x)=u_0(x)$, $x\in\mathbf{R}$, with a super critical nonlinearity $f(u)=\sum_{j\neq 0}f_j(u)$, and $f_j(u)$ are such that $f_j(u)=\lambda_j\vert u\vert^{\sigma_j-j}u^j$, where $\lambda_j\in\mathbf{C}$, $\sigma_j>3$. We prove the existence of the scattering operator in the weighted Sobolev spaces. Scattering operator, Asymptotic behavior in time, Nonlinear Schrödinger, Power nonlinearity. 35Q55, 35B40. 58-451 2015 Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d Nakao HAYASHI and Pavel I. NAUMKIN Nakao HAYASHI and Pavel I. NAUMKIN 1 Bergh, J.; Löfström, J. Interpolation spaces. An introduction Grundlehren der Mathematischen Wissenschaften, No. 223. Springer-Verlag, Berlin-New York 1976 MR0482275 2 Cazenave, Th. Semilinear Schrödinger equations Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI 2003 MR2002047
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