کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1899873 | 1534067 | 2009 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Coupled mode equations and gap solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schrödinger/Gross-Pitaevskii Equation with a non-separable potential of finite contrast. We show that unlike in the case of separable potentials [T. Dohnal, D. Pelinovsky, G. Schneider, Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential, J. Nonlinear Sci. 19 (2009) 95-131] the CME derivation has to be carried out in Bloch rather than physical coordinates. Using the Lyapunov-Schmidt reduction we then give a rigorous justification of the CMEs as an asymptotic model for reversible non-degenerate gap solitons and provide Hs estimates for this approximation. The results are confirmed by numerical examples, including some new families of CMEs and gap solitons absent for separable potentials.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 238, Issues 9â10, 15 May 2009, Pages 860-879
Journal: Physica D: Nonlinear Phenomena - Volume 238, Issues 9â10, 15 May 2009, Pages 860-879
نویسندگان
TomáÅ¡ Dohnal, Hannes Uecker,