Inverse scattering for the nonlinear Schrodinger equation with the Yukawa potential

被引：5

作者：

Sasaki, Hironobu ^{[1
]}

机构：

[1] Osaka Univ, Dept Math, Osaka 5630043, Japan

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2008年 / 33卷 / 07期

基金：

日本学术振兴会;

关键词：

inverse scattering; nonlinear Schrodinger equation; semi-relativistic Hartree equation; Yukawa potential;

D O I：

10.1080/03605300701790245

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the inverse scattering problem for the three dimensional nonlinear Schrodinger equation with the Yukawa potential. The nonlinearity of the equation is nonlocal. We reconstruct the potential and the nonlinearity by the knowledge of the scattering states. Our result is applicable to reconstructing the nonlinearity of the semi-relativistic Hartree equation.

引用

页码：1175 / 1197

页数：23

共 50 条

[1] Inverse scattering for the nonlinear Schrodinger equation
Weder, R
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1997, 22 (11-12) : 2089 - 2103
[2] Uniqueness of inverse scattering for the nonlinear Schrodinger equation and reconstruction of the potential and the nonlinearity
Weder, R
[J]. FIFTH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION, 2000, : 631 - 634
[3] Lp-Lp estimates for the Schrodinger equation on the line and inverse scattering for the nonlinear schrodinger equation with a potential
Weder, R
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 170 (01) : 37 - 68
[4] SCATTERING FOR A NONLINEAR SCHRODINGER EQUATION WITH A POTENTIAL
Hong, Younghun
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (05) : 1571 - 1601
[5] Inverse scattering transformation for generalized nonlinear Schrodinger equation
Zhang, Xiaoen
Chen, Yong
[J]. APPLIED MATHEMATICS LETTERS, 2019, 98 : 306 - 313
[6] Inverse scattering transform for the derivative nonlinear Schrodinger equation
Yang Chun-Nuan
Yu Jia-Lu
Cai Hao
Huang Nian-Ning
[J]. CHINESE PHYSICS LETTERS, 2008, 25 (02) : 421 - 424
[7] Inverse scattering for a Schrodinger equation with energy dependent potential
van der Mee, C
Pivovarchik, V
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2001, 42 (01) : 158 - 181
[8] The nonlinear Schrodinger equation with an inverse-square potential
Murphy, Jason
[J]. NONLINEAR DISPERSIVE WAVES AND FLUIDS, 2019, 725 : 215 - 225
[9] Inverse scattering transform for the integrable nonlocal nonlinear Schrodinger equation
Ablowitz, Mark J.
Musslimani, Ziad H.
[J]. NONLINEARITY, 2016, 29 (03) : 915 - 946
[10] Inverse scattering on the line for a generalized. nonlinear Schrodinger equation
Aktosun, T
Papanicolaou, VG
Zisis, V
[J]. INVERSE PROBLEMS, 2004, 20 (04) : 1267 - 1280

← 1 2 3 4 5 →