D. Blackmore, A. K. Prykarpatsky
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised. The relationship with the Lie-algebraic integrability scheme is analyzed, the connection with the tau-function representation is briefly discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose some properties of these equations and also briefly study a stochastic Camassa-Holm equation which reduces…
Quasiclassical integrability condition in AKNS scheme
本文研究孤子方程的准经典可积性条件，并证明载波波数函数与线性谐波色散关系共同决定AKNS框架标量表示中Lax对函数的准经典极限。
The two matrix spectral problems of Ablowitz-Kaup-Newell-Segur (AKNS) and Kaup-Newell (KN) types associated with so(3,R) are generalized. The corresponding hierarchies of generalized soliton equations are derived by the standard procedure using the zero curvature formulation. Recursion operators and bi-Hamiltonian structures are explicitly constructed for the resulting two generalized soliton hierarchies of AKNS and KN types, which shows their Liouville integrability.
A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax type representation and Poisson structures constructed in exact form. The related bi-Hamiltonian integrability and compatible Poissonian structures of the generalized Riemann type hierarchy are also discussed.
Two multicomponent generalizations of the AKNS-type spectral problems associated with $sl(2,\mathbb{R})$ and $so(3,\mathbb{R})$ are introduced and the corresponding two hierarchies of generalized multicomponent AKNS-type soliton equations are presented by the standard procedure, respectively. By virtue of the trace identity, bi-Hamiltonian structures which lead to a common recursion operator are established for each of the two resulting soliton hierarchies. And thus the Liouville integrability is shown for all systems in each of the two new generalized soliton hierarchies, seperately.
We further generalize the generalized short pulse equation studied recently in [Commun. Nonlinear Sci. Numer. Simulat. 39 (2016) 21-28; arXiv:1510.08822], and find in this way two new integrable nonlinear wave equations which are transformable to linear Klein-Gordon equations.
In this paper we will discuss some features of the bihamiltonian method for solving the Hamilton-Jacobi (H-J) equations by Separation of Variables, and make contact with the theory of Algebraic Complete Integrability and, specifically, with the Veselov--Novikov notion of algebro-geometric (AG) Poisson brackets. The "bihamiltonian" method for separating the Hamilton-Jacobi equations is based on the notion of pencil of Poisson brackets and on the Gel'fand-Zakharevich (GZ) approach to integrable systems. We will herewith show how, quite naturally, GZ systems may give rise to AG Poisson brackets, …
We develop a systematic approach to the classical Boussinesq (cBsq) hierarchy based on an elementary polynomial recursion formalism. Moreover, the gauge equivalence between the cBsq and AKNS hierarchies is studied in detail and used to provide an effortless derivation of algebro-geometric solutions and their theta function representations of the cBsq hierarchy.
Only the known integrable cases of the Kodama-Hasegawa higher-order nonlinear Schroedinger equation pass the Painleve test. Recent results of Ghosh and Nandy add no new integrable cases of this equation.
Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.
The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and \textit{}extended to the AKNS/Lund-Regge model and to its corresponding supersymmetric versions. The integrability of the models is guaranteed from the zero curvature representation and some soliton solutions are discussed.
Moving null curves and integrability
本文研究三维平坦时空中零曲线运动形成曲面的可积性，证明其条件对应 AKNS 层级，并构造 MKdV 孤子曲面、分析曲率奇点及 Heisenberg 自旋方程。
The Lax pair formalism is considered to discuss the integrability of the N=1 supersymmetric sinh-Gordon model with a defect. We derive associated defect matrix for the model and construct the generating functions of the modified conserved quantities. The corresponding defect contributions for the modified energy and momentum of the model are explicitly computed.
Poisson-Lie analogues of spin Sutherland models revisited
本文重新研究紧半单李群 Heisenberg double 上主可积系统的 Poisson 约化，严格证明约化系统在主轨道型稠密开集及一般辛叶上的退化可积性，并给出约化 Poisson 结构与标度极限的新描述。
We bring together aspects of covariant Hamiltonian field theory and of classical integrable field theories in $1+1$ dimensions. Specifically, our main result is to obtain for the first time the classical $r$-matrix structure within a covariant Poisson bracket for the Lax connection, or Lax one form. This exhibits a certain covariant nature of the classical $r$-matrix with respect to the underlying spacetime variables. The main result is established by means of several prototypical examples of integrable field theories, all equipped with a Zakharov-Shabat type Lax pair. Full details are present…
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Po…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。