The Cauchy problem for defocusing nonlinear Schrodinger equations with non-vanishing initial data at infinity

被引：38

作者：

Gallo, Clement ^{[1
]}

机构：

[1] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 33卷 / 05期

关键词：

dark solitons; initial value problem; nonlinear Schrodinger equations;

D O I：

10.1080/03605300802031614

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For rather general nonlinearities, we prove that defocusing nonlinear Schrdinger equations in R(n) (n <= 4), with non-vanishing initial data at infinity u(0), are globally well-posed in u(0) + H(1). The same result holds in an exterior domain in R(n), n = 2, 3.

引用

页码：729 / 771

页数：43

共 50 条

[31] Groundstates for the nonlinear Schrodinger equation with potential vanishing at infinity
Bonheure, Denis
Van Schaftingen, Jean
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2010, 189 (02) : 273 - 301
[32] The cauchy problem of the nonlinear schrodinger equations in R1+1
Xu, Gui-xiang
[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2007, 23 (04): : 593 - 610
[33] BLOWING UP OF SOLUTIONS TO CAUCHY-PROBLEM FOR NONLINEAR SCHRODINGER EQUATIONS
GLASSEY, RT
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1977, 18 (09) : 1794 - 1797
[34] Cauchy problem for nonlinear Schrodinger equations with inverse-square potentials
Okazawa, Noboru
Suzuki, Toshiyuki
Yokota, Tomomi
[J]. APPLICABLE ANALYSIS, 2012, 91 (08) : 1605 - 1629
[35] Nonlinear Cauchy problem with slowly oscillating initial data
Gourdin, D
Mechab, M
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2001, 125 (05): : 371 - 394
[36] NODAL SOLUTIONS OF 2-D CRITICAL NONLINEAR SCHRODINGER EQUATIONS WITH POTENTIALS VANISHING AT INFINITY
Fei, Mingwen
Yin, Huicheng
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (07) : 2921 - 2948
[37] ON NONLINEAR SCHRODINGER EQUATIONS WITH ALMOST PERIODIC INITIAL DATA
Oh, Tadahiro
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2015, 47 (02) : 1253 - 1270
[38] SOLUTIONS TO NONLINEAR SCHRODINGER EQUATIONS FOR SPECIAL INITIAL DATA
Wada, Takeshi
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[39] ON THE RADIUS OF SPATIAL ANALYTICITY FOR DEFOCUSING NONLINEAR SCHRODINGER EQUATIONS
Ahn, Jaeseop
Kim, Jimyeong
Seo, Ihyeok
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (01) : 423 - 439
[40] GLOBAL WELL-POSEDNESS OF THE GROSS-PITAEVSKII AND CUBIC-QUINTIC NONLINEAR SCHRODINGER EQUATIONS WITH NON-VANISHING BOUNDARY CONDITIONS
Killip, Rowan
Oh, Tadahiro
Pocovnicu, Oana
Visan, Monica
[J]. MATHEMATICAL RESEARCH LETTERS, 2012, 19 (05) : 969 - 986

← 1 2 3 4 5 →