General soliton solution to a nonlocal nonlinear Schrodinger equation with zero and nonzero boundary conditions

被引：142

作者：

Feng, Bao-Feng ^{[1
]}

Luo, Xu-Dan ^{[2
]}

Ablowitz, Mark J. ^{[3
]}

Musslimani, Ziad H. ^{[4
]}

机构：

[1] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

[2] SUNY Buffalo, Dept Math, Buffalo, NY 14260 USA

[3] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

[4] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

来源：

NONLINEARITY | 2018年 / 31卷 / 12期

关键词：

nonlocal nonlinear Schrodiinger equation; Hirota's bilinear method; the KP hierarchy reduction method; soliton solutions with zero and nonzero boundary conditions; INVERSE SCATTERING TRANSFORM; DISPERSIVE DIELECTRIC FIBERS; DE-VRIES EQUATION; OPTICAL PULSES; MANAKOV SYSTEM; KP HIERARCHY; TRANSMISSION; DYNAMICS; WAVES;

D O I：

10.1088/1361-6544/aae031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

General soliton solutions to a nonlocal nonlinear Schrodinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions are considered via the combination of Hirota's bilinear method and the Kadomtsev-Petviashvili (KP) hierarchy reduction method. First, general N-soliton solutions with zero boundary conditions are constructed. Starting from the tau functions of the two-component KP hierarchy, it is shown that they can be expressed in terms of either Gramian or double Wronskian determinants. On the contrary, from the tau functions of single component KP hierarchy, general soliton solutions to the nonlocal NLS equation with nonzero boundary conditions are obtained. All possible soliton solutions to nonlocal NLS with Parity (PT)-symmetry for both zero and nonzero boundary conditions are found in the present paper.

引用

页码：5385 / 5409

页数：25

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