具有外势的非等谱可积非线性方程及其 GBDT 解
可精确求解与可积系统
2008-04-02 v1
摘要
引入了矩阵非等谱方程的辅助系统,包括具有外势的耦合 NLS 方程和具有变系数的 KdV 方程。利用 Bäcklund-Darboux 变换的 GBDT 版本,构造了非等谱方程的显式解。
引用
@article{arxiv.0710.2260,
title = {Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:0710.2260},
year = {2008}
}
相关论文
查看更多相关论文 →
经典分析与常微分方程 · 数学
GBDT, multiplicative integrals and linear similarity
Alexander Sakhnovich
2025-04-01
偏微分方程分析 · 数学
Einstein, $\sigma$-model and Ernst-type equations and non-isospectral GBDT version of Darboux transformation
Alexander Sakhnovich
2024-04-03
偏微分方程分析 · 数学
Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches
J. Michor, A. L. Sakhnovich
2020-07-03
经典分析与常微分方程 · 数学
On the GBDT version of the B\"acklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory
Alexander Sakhnovich
2011-04-05
偏微分方程分析 · 数学
Generalized Baecklund-Darboux transformation: conservation laws, rational extensions and bispectrality
Alexander Sakhnovich
2016-11-03
数学物理 · 物理学
B\"acklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem
Alexander Sakhnovich
2008-04-24
偏微分方程分析 · 数学
GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases)
Roman O. Popovych, Alexander Sakhnovich
2019-07-22
经典分析与常微分方程 · 数学
Explicit solutions of Schr\"odinger and KdV equations in terms of square roots of the generalised matrix eigenvalues
Alexander Sakhnovich
2024-04-03
可精确求解与可积系统 · 物理学
GBDT with nontrivial seeds: explicit solutions of the focusing NLS equations and the corresponding Weyl functions
Alexander Sakhnovich
2025-06-10
可精确求解与可积系统 · 物理学
Negaton and Positon solutions of the soliton equation with self-consistent sources
Yunbo Zeng, Yijun Shao, Weimin Xue
2009-11-10
可精确求解与可积系统 · 物理学
Cauchy matrix structures and solutions to the nonisospectral three-component mKdV equations
Mengli Tian, Chunxia Li, Yue Li, Fei Li +1
2025-09-01
动力系统 · 数学
Continuous and discrete dynamical Schr\"odinger systems: explicit solutions
B. Fritzsche, B. Kirstein, I. Ya. Roitberg, A. L. Sakhnovich
2018-03-20
经典分析与常微分方程 · 数学
GBDT of discrete skew-selfadjoint Dirac systems and explicit solutions of the corresponding non-stationary problems
Alexander Sakhnovich
2020-07-03
数学物理 · 物理学
Nonlocal symmetries related to B\"acklund transformation and their applications
S. Y. Lou, Xiaorui Hu, Yong Chen
2012-01-18
可精确求解与可积系统 · 物理学
Exact solutions of multicomponent nonlinear Schr\"odinger equations under general plane-wave boundary conditions
Takayuki Tsuchida
2013-10-25
数学物理 · 物理学
Exterior Differential Systems, Prolongations and the Integrability of Two Nonlinear Partial Differential Equations
Paul Bracken
2009-03-25
可精确求解与可积系统 · 物理学
The general solutions for a non-isospectral integrable TD hierarchy via the inverse scattering transform
Hongyi Zhang, Yufeng Zhang, Binlu Feng
2023-11-21
泛函分析 · 数学
On the factorization formula for fundamental solutions in the inverse spectral transform
Alexander Sakhnovich
2012-11-29
数学物理 · 物理学
B\"{a}cklund and Darboux transformations for the nonstationary Schr\"{o}dinger equation
M. Boiti, F. Pempinelli, A. Pogrebkov, B. Prinari
2007-05-23
可精确求解与可积系统 · 物理学
Algebraic construction of the Darboux matrix revisited
Jan L. Cieslinski
2015-05-13
数学物理 · 物理学
Darboux Transformation for the Non-isospectral AKNS Hierarchy and Its Asymptotic Property
Lingjun Zhou
2009-11-13
综合数学 · 数学
B\"acklund Transformations: Some Old and New Perspectives
C. J. Papachristou, A. N. Magoulas
2023-07-21
可精确求解与可积系统 · 物理学
On a new integrable nonlinear Schroedinger equation with a simple external potential and its explicit solutions
Alexander Sakhnovich
2007-05-23
可精确求解与可积系统 · 物理学
A supersymmetric AKNS problem and its Darboux-B\"acklund transformations and discrete systems
Lingling Xue, Q. P. Liu
2016-02-19
可精确求解与可积系统 · 物理学
B\"acklund-Darboux Transformations and Discretizations of $N=2\; a=-2$ Supersymmetric KdV Equation
Hui Mao, Q. P. Liu
2018-01-17