A nonlocal finite-dimensional integrable system related to the nonlocal nonlinear Schrödinger equation hierarchy

被引：3

作者：

Wang, Xue ^{[1
]}

Du, Dianlou ^{[2
]}

机构：

[1] Henan Univ Engn, Coll Sci, Zhengzhou 451191, Henan, Peoples R China

[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2024年 / 21卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Nonlocal integrable system; NNLS equation; action-angle variables; Lie-Poisson Hamiltonian systems; INVERSE SCATTERING; SOLITON-SOLUTIONS; RESTRICTED FLOWS; COUPLED KDV; STATIONARY;

D O I：

10.1142/S0219887824500452

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Based on the Lenard gradient sequence, a hierarchy of the nonlocal nonlinear Schrodinger (NNLS) equations is obtained. Using the Lax representation, the nonlocal finite-dimensional integrable system with Lie-Poisson structure is presented. Then, under coordinate transformation, the nonlocal finite-dimensional integrable system with Lie-Poisson structure can be expressed as the canonical Hamiltonian system of the standard symplectic structures. Moreover, the parametric representation of the NNLS equation and the nonlocal complex modified Kortewegde Vries (NcmKdV) equation are constructed. Finally, according to the Hamilton-Jacobi theory, the action-angle variables are built and the inversion problem related to the Lie-Poisson Hamiltonian systems is discussed.

引用

页数：34

共 50 条

[31] Finite-Dimensional Integrable Hamiltonian Systems Related to the Nonlinear Schrodinger Equation
Zhou, Ruguang
STUDIES IN APPLIED MATHEMATICS, 2009, 123 (04) : 311 - 335
[32] Riemann–Hilbert approach and nonlinear dynamics in the nonlocal defocusing nonlinear Schrödinger equation
Jianping Wu
The European Physical Journal Plus, 135
[33] Accessible solitary wave families of the generalized nonlocal nonlinear Schrödinger equation
W.-P. Zhong
M. Belić
T. W. Huang
R. H. Xie
The European Physical Journal D, 2010, 59 : 301 - 304
[34] Life span of solutions to a nonlocal in time nonlinear fractional Schrödinger equation
M. Kirane
A. Nabti
Zeitschrift für angewandte Mathematik und Physik, 2015, 66 : 1473 - 1482
[35] Dynamics of solitons in the fourth-order nonlocal nonlinear Schrödinger equation
T. A. Gadzhimuradov
A. M. Agalarov
R. Radha
B. Tamil Arasan
Nonlinear Dynamics, 2020, 99 : 1295 - 1300
[36] Soliton solutions of the space–time fractional nonlocal nonlinear Schrödinger equation
Zhang L.
Liu H.
Optik, 2023, 289
[37] Exotic localized waves in the shifted nonlocal multicomponent nonlinear Schrödinger equation
Xiu-Bin Wang
Shou-Fu Tian
Theoretical and Mathematical Physics, 2022, 212 : 1193 - 1210
[38] Spatiotemporal Hermite–Gaussian solitons of a (3 + 1)-dimensional partially nonlocal nonlinear Schrödinger equation
Chao-Qing Dai
Yu Wang
Jiu Liu
Nonlinear Dynamics, 2016, 84 : 1157 - 1161
[39] Riemann–Hilbert approach and soliton classification for a nonlocal integrable nonlinear Schrödinger equation of reverse-time type
Jianping Wu
Nonlinear Dynamics, 2022, 107 : 1127 - 1139
[40] On a periodic Schrödinger equation with nonlocal superlinear part
Nils Ackermann
Mathematische Zeitschrift, 2004, 248 : 423 - 443

← 1 2 3 4 5 →