The derivation of the conservation law for defocusing nonlinear Schrodinger equations with non-vanishing initial data at infinity

被引：3

作者：

Miyazaki, Hayato ^{[1
]}

机构：

[1] Hiroshima Univ, Grad Sch Sci, Dept Math, Higashihiroshima 7894521, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 417卷 / 02期

关键词：

Gross-Pitaevskii equation; Cubic-quintic nonlinear Schrodinger equations; Non-vanishing boundary condition; Conservation laws; CAUCHY-PROBLEM; SOLITONS;

D O I：

10.1016/j.jmaa.2014.03.055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For nonlinear Schrodinger equations in less than or equal to four dimension, with non-vanishing initial data at infinity, a new approach to derive the conservation law is obtained. Since this approach does not contain approximating procedure, the argument is simplified and some of technical assumption of the nonlinearity to derive the conservation law and time global solutions, is removed. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：580 / 600

页数：21

共 50 条

[1] The Cauchy problem for defocusing nonlinear Schrodinger equations with non-vanishing initial data at infinity
Gallo, Clement
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (05) : 729 - 771
[2] Nonlinear Schrodinger equations with potentials vanishing at infinity
Bonheure, D
Van Schaftingen, J
[J]. COMPTES RENDUS MATHEMATIQUE, 2006, 342 (12) : 903 - 908
[3] Conservation laws for the derivative nonlinear Schrodinger equation with non-vanishing boundary conditions
Chen, XJ
Hou, LJ
Lam, WK
[J]. CHINESE PHYSICS LETTERS, 2005, 22 (04) : 830 - 832
[4] On the Whitham Equations for the Defocusing Nonlinear Schrodinger Equation with Step Initial Data
G. Biondini
Y. Kodama
[J]. Journal of Nonlinear Science, 2006, 16 : 435 - 481
[5] On the Whitham equations for the defocusing nonlinear Schrodinger equation with step initial data
Biondini, G.
Kodama, Y.
[J]. JOURNAL OF NONLINEAR SCIENCE, 2006, 16 (05) : 435 - 481
[6] Stationary nonlinear Schrodinger equations in with potentials vanishing at infinity
do O, Joao Marcos
Sani, Federica
Zhang, Jianjun
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2017, 196 (01) : 363 - 393
[7] GLOBAL EXISTENCE FOR THE DEFOCUSING NONLINEAR SCHRODINGER EQUATIONS WITH LIMIT PERIODIC INITIAL DATA
Oh, Tadahiro
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2015, 14 (04) : 1563 - 1580
[8] Ground states of nonlinear Schrodinger equations with potentials vanishing at infinity
Ambrosetti, A
Felli, V
Malchiodi, A
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2005, 7 (01) : 117 - 144
[9] Bound states of nonlinear Schrodinger equations with potentials vanishing at infinity
Ambrosetti, A.
Malchiodi, A.
Ruiz, D.
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 2006, 98 (1): : 317 - 348
[10] Remarks on a Class of Nonlinear Schrodinger Equations with Potential Vanishing at Infinity
Zhu, Hongbo
[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2013, 2013

← 1 2 3 4 5 →