SOLUTIONS OF GROSS-PITAEVSKII EQUATION WITH PERIODIC POTENTIAL IN DIMENSION THREE

被引：1

作者：

Karpeshina, YU. ^{[1
]}

Kim, Seonguk ^{[2
]}

Shterenberg, R. ^{[2
]}

机构：

[1] Univ Alabama Birmingham, Dept Math, Campbell Hall,1300 Univ Blvd, Birmingham, AL 35294 USA

[2] Defiance Coll, Div Nat Sci Appl Sci & Math, Defiance, OH 43512 USA

来源：

ST PETERSBURG MATHEMATICAL JOURNAL | 2024年 / 35卷 / 01期

关键词：

Bose-Einstein condensate; quasiperiodic solution; quasimomentum; plane wave;

D O I：

10.1090/spmj/1798

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Quasiperiodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proved that there is an extensive "nonresonant" set G subset of R-3 such that for every k(->) is an element of G there is a solution asymptotically close to a plane wave Ae(i) (k(->), x(->)) as |k(->)| -> infinity, given A is sufficiently small.

引用

页码：153 / 169

页数：17

共 10 条

[1]

[Anonymous], 1965, Principles of the theory of solids

[2]

Karpeshina Y. E., 1997, LECT NOTES MATH, V1663

[3]

Karpeshina Yu. E., 2020, OPER THEORY ADV APPL, V276, P401

[4]

Kittel Charles, 1976, INTRO SOLID STATE PH

[5] Modulational instability in Bose-Einstein condensates in optical lattices [J].

Konotop, VV ;

Salerno, M .

PHYSICAL REVIEW A, 2002, 65 (02) :1-4

[6] Bose-Einstein condensates in optical lattices: Band-gap structure and solitons [J].

Louis, PJY ;

Ostrovskaya, EA ;

Savage, CM ;

Kivshar, YS .

PHYSICAL REVIEW A, 2003, 67 (01) :9

[7]

Madelung O., 1978, Introduction to solid-state theory

[8]

Pethick CJ, 2008, BOSE-EINSTEIN CONDENSATION IN DILUTE GASES, P1

[9] Superfluidity breakdown of periodic matter waves in quasi-one-dimensional annular traps via resonant scattering with moving defects [J].

Yulin, A. V. ;

Bludov, Yu. V. ;

Konotop, V. V. ;

Kuzmiak, V. ;

Salerno, M. .

PHYSICAL REVIEW A, 2013, 87 (03)

[10] Out-of-gap Bose-Einstein solitons in optical lattices [J].

Yulin, AV ;

Skryabin, DV .

PHYSICAL REVIEW A, 2003, 67 (02) :8

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