Abstract
We study the final value problem for the nonlinear Schrödinger equations in one or two space dimensions with the gauge-invariant nonlinearity of the critical long-range power and nonresonant polynomial nonlinearities of the same power, which are not gauge invariant. We construct a unique global solution (for positive time) which is asymptotic for large time to a given profile with sufficiently small norm in lower order Sobolev spaces with decay at the spatial infinity and at the zero frequency.
Original language | English |
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Pages (from-to) | 759-775 |
Number of pages | 17 |
Journal | Journal of Hyperbolic Differential Equations |
Volume | 8 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2011 Dec |
Externally published | Yes |
Keywords
- Modified wave operators
- lower order Sobolev
- nonlinear Schrödinger equations
ASJC Scopus subject areas
- Analysis
- Mathematics(all)