Carles, Rémi; Nakamura, Yoshihisa Nonlinear Schrödinger equations with Stark potential. (English) Zbl 1069.35083 Hokkaido Math. J. 33, No. 3, 719-729 (2004). Summary: We study the nonlinear Schrödinger equations with a linear potential \[ i\varepsilon\partial_tu+\frac 12\varepsilon^2 \Delta u=V(x)u+\lambda |u|^{2\sigma}u,\quad u|_{t=0}= u_0. \] A change of variables makes it possible to deduce results concerning finite time blow up and scattering theory from the case with no potential. Cited in 6 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 81U05 \(2\)-body potential quantum scattering theory 35P25 Scattering theory for PDEs Keywords:Stark effect; Avron-Herbst formula; pseudo-conformal conversation law; finite time blow up × Cite Format Result Cite Review PDF Full Text: DOI arXiv