کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10224103 1701076 2018 54 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The nonlinear Schrödinger equation with a potential
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
The nonlinear Schrödinger equation with a potential
چکیده انگلیسی
We consider the cubic nonlinear Schrödinger equation with a potential in one space dimension. Under the assumptions that the potential is generic, sufficiently localized, with no bound states, we obtain the long-time asymptotic behavior of small solutions. In particular, we prove that, as time goes to infinity, solutions exhibit nonlinear phase corrections that depend on the scattering matrix associated to the potential. The proof of our result is based on the use of the distorted Fourier transform - the so-called Weyl-Kodaira-Titchmarsh theory - a precise understanding of the “nonlinear spectral measure” associated to the equation, and nonlinear stationary phase arguments and multilinear estimates in this distorted setting.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincaré C, Analyse non linéaire - Volume 35, Issue 6, September 2018, Pages 1477-1530
نویسندگان
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