Hamilton-Jacobi equations with jumps: asymptotic stability
Amir Mahmood, Saima Parveen
本文将根据跳跃控制函数的强耗散性，并利用可微流的轨道描述相应的特征系统，分析满足带跳跃的Hamilton-Jacobi方程整体解的渐近稳定性。
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe the corresponding characteristic system.
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In this paper, we propose a discrete Hamilton--Jacobi theory for (discrete) Hamiltonian dynamics defined on a (discrete) contact manifold. To this end, we first provide a novel geometric Hamilton--Jacobi theory for continuous contact Hamiltonian dynamics. Then, rooting on the discrete contact Lagrangian formulation, we obtain the discrete equations for Hamiltonian dynamics by the discrete Legendre transformation. Based on the discrete contact Hamilton equation, we construct a discrete Hamilton--Jacobi equation for contact Hamiltonian dynamics. We show how the discrete Hamilton--Jacobi equation…
A Hamilton-Jacobi Theory for Singular Lagrangian Systems in the Skinner and Rusk Setting
我们在Skinner-Rusk形式主义中发展了奇异拉格朗日系统的Hamilton-Jacobi理论。比较与哈密顿-雅可比问题的拉格朗日和哈密顿设置进行了讨论。
Generalized Hamilton-Jacobi equations for nonholonomic dynamics
采用适当的非线性Lagrange泛函，我们推导出线性速度约束下动力系统的广义Hamilton-Jacobi方程。只要广义哈密顿-雅可比方程的解存在，作用量实际上是最小化的（而不仅仅是极值化的）。
In this paper we propose a geometric Hamilton--Jacobi theory on a Nambu--Jacobi manifold. The advantange of a geometric Hamilton--Jacobi theory is that if a Hamiltonian vector field $X_H$ can be projected into a configuration manifold by means of a one-form $dW$, then the integral curves of the projected vector field $X_H^{dW}$ can be transformed into integral curves of the vector field $X_H$ provided that $W$ is a solution of the Hamilton--Jacobi equation. This procedure allows us to reduce the dynamics to a lower dimensional manifold in which we integrate the motion. On the other hand, the i…
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express and prove two geometric version of the Hamilton-Jacobi theorem for Hamiltonian system on Lie algebroids. Then this results are generalized and two types of time-dependent Hamilton-Jacobi theorem of Hamiltonian system on Lie algebroids are obtained.
The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given Hamiltonian function. We also analyze the corresponding formulation on the symplectification of the contact Hamiltonian system, and establish the relations between these two approaches. In the last section, some examples are discussed.
The relation between the canonical Hamilton-Jacobi equation and the covariant Hamilton-Jacobi equation for Maxwell's electrodynamics
本文通过时空分裂方法，从协变Hamilton-Jacobi方程推导出麦克斯韦电动力学的正则Hamilton-Jacobi方程及高斯定律约束，并探讨其对标准量子化与前正则量子化联系的准经典极限分析的意义。
Recently, M. de León el al. ([8]) have developed a geometrical description of Hamilton-Jacobi theory for multisymplectic field theory. In our paper we analyse in the same spirit a special kind of field theories which are gauge field theories. The Hamilton-Jacobi theory for this kind of fields is shown.
Hamilton-Jacobi theory in k-cosymplectic field theories
本文将含时力学的Hamilton-Jacobi理论的几何形式推广到经典场论的k-共辛框架中。
Hamilton-Jacobi theory in Cauchy data space
最近，M。de León等（[9]）在多辛几何的背景下发展了经典场论的几何Hamilton-Jacobi理论。本文的目的是在柯西数据空间中建立相应的Hamilton-Jacobi理论，并将这两种方法联系起来。
A Geometric Hamilton-Jacobi Theory for Classical Field Theories
本文在多辛几何和Ehresmann联络的框架下，将哈密顿力学的Hamilton-Jacobi理论的几何形式推广到经典场论的情形。
On the Hamilton-Jacobi Theory for Singular Lagrangian Systems
我们开发了一个奇异拉格朗日系统的Hamilton Jacobi理论使用Gotay-Nester-Hinds约束算法。即使系统具有次级约束，该过程也有效。
Non-standard Construction of Hamiltonian Structures and of the Hamilton-Jacobi equation
给出了动力系统的哈密顿结构的非标准构造和相应的哈密顿-雅可比（H-J）方程的例子，而不使用拉格朗日量。欧拉顶的替代H-J方程显式展示和解决。我们表明，一些稳定性标准，相关的斜率的Casimir函数参数化的拉格朗日乘子临界点类型，取决于所使用的哈密顿结构，这是不够的，因为这个原因。
Hamilton-Jacobi Fractional Sequential Mechanics
作为Rabei等人[11]工作的继续，将Hamilton- Jacobi偏微分方程推广到适用于含分数阶导数的系统。位形空间中的Hamilton- Jacobi函数是以与通常力学类似的方式得到的.两个问题被认为是证明的形式主义的应用。结果与Agrawal的形式主义完全一致。
Geometric Hamilton-Jacobi theory for higher-order autonomous systems
哈密顿-雅可比理论的几何框架是用来研究这一理论的环境中的高阶力学系统，无论是在拉格朗日和哈密顿形式主义。因此，我们在这些形式中陈述相应的Hamilton-Jacobi方程，并应用我们的结果来分析一些特定的物理例子。
Lagrangian submanifolds and Hamilton-Jacobi equation
拉格朗日子流形正成为推广和几何理解数学物理领域中的结果和过程的一个非常重要的工具。在这里，我们使用一般的拉格朗日子流形提供一个几何版本的汉密尔顿-雅可比方程。这种解释使我们能够从几何的观点研究Hamilton-Jacobi方程在完整、非完整和含时动力学中的一些有趣的应用。
Existence of solutions for Hamiltonian field theories by the Hamilton-Jacobi technique
本文证明了场论中Hamilton-Jacobi方程局部解的存在性，从而得到了场方程的通解。该解决方案是适应的选择的子流形的初始数据的场方程被分配。最后，从给定的初始流形出发，推导出一种求场方程通解的方法。
Hamilton-Jacobi Theory in k-Symplectic Field Theories
本文将力学的Hamilton-Jacobi理论的几何形式推广到经典场论在k-辛框架下的情形。
Hamilton-Jacobi Formalism on Locally Conformally Symplectic Manifolds
该研究构建了局部共形辛流形上的Hamilton-Jacobi形式体系，先给出局部版本再借助Lichnerowicz-deRham微分实现全局描述，揭示了局部与全局理论的关联。
In this paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$ generated by Morse families. The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton--Jacobi equation is obtained with the aid of this generating family of functions. To conclude, we apply our results to sin…
Hamilton-Jacobi theory for one dimensional autonomous systems using parametric transformations
得到了一维自治系统能量保持不变的参数变换的一个充要条件。利用参数变换，用求积法求解Hamilton-Jacobi方程。给出了这种方法的一个例子。
The Hamilton-Jacobi [$HJ$] analysis for higher-order Chern-Simons gravity is performed. The complete set of $HJ$ Hamiltonians are identified and a fundamental $HJ$ differential is constructed, from which the characteristic equations are obtained. In addition, the symmetries of the theory are identified and the obtained results are compared with other approaches reported in the literature.
Analogs of the Hamilton-Jacobi and Schrodinger Equations for Multidimensional Variational Problems of Field Theory
本文导出了场论多维变分问题的Hamilton-Jacobi方程和Schrodinger方程的推广。这些推广就是所谓的变分微分方程。
Unified formalism for the generalized kth-order Hamilton-Jacobi problem
哈密顿-雅可比理论的几何表述使我们能够将其推广到高阶常微分方程组。在这项工作中，我们介绍了统一的拉格朗日-哈密顿形式主义的几何哈密顿-雅可比理论的高阶自治动力系统所描述的正则拉格朗日函数。
The Hamilton-Jacobi equation on Lie affgebroids
介绍了李仿射体上哈密顿截面的哈密顿-雅可比方程，并给出了一些例子。
A Universal Hamilton-Jacobi Theory
本文在几乎Poisson流形的背景下发展了一个Hamilton-Jacobi理论。该理论推广了经典的Hamilton-Jacobi理论，也可应用于非常一般的情况，包括非完整力学系统和含外力的时变系统。
In this survey, we review the classical Hamilton Jacobi theory from a geometric point of view in different geometric backgrounds. We propose a Hamilton Jacobi equation for different geometric structures attending to one particular characterization: whether they fulfill the Jacobi and Leibniz identities simultaneously, or if at least they satisfy one of them. In this regard, we review the case of time dependent and dissipative physical systems as systems that fulfill the Jacobi identity but not the Leibnitz identity. Furthermore, we review the contact evolution Hamilton Jacobi theory as a split…
Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints
我们将Hamilton-Jacobi理论推广到拉格朗日-狄拉克（或隐式拉格朗日）系统，这是一种广义的拉格朗日力学公式，它可以包含退化拉格朗日以及完整和非完整约束。我们把广义的Hamilton-Jacobi方程称为Dirac-Hamilton-Jacobi方程。对于具有非完整约束的非退化拉格朗日系统，该理论专门针对最近发展的非完整Hamilton-Jacobi理论。我们特别感兴趣的应用程序的某一类退化的非完整拉格朗日系统的对称性，我们称之为弱退化Chaubergin系统，出现的简化模型的非完整力学系统，这些系统被证明是减少到非退化的几乎哈密顿系统，即，用非闭二形式定义的广义Hamilton系统。因此，狄拉克-汉密尔顿-雅可比方程简化为与简化系统相关的非完整汉密尔顿-雅可比方程的变体。我们通过几个例子来说明如何Dirac-Hamilton-Jacobi方程可以用来精确地集成的运动方程。
Hamilton-Jacobi theory, Symmetries and Coisotropic Reduction
约化理论在哈密顿系统的研究中起着重要的作用。另一方面，Hamilton-Jacobi理论是集成某些哈密顿问题的动力学的主要工具之一，并且其本身也是一个研究课题。此外，几个辛积分器的建设依赖于一个完整的解决方案的Hamilton-Jacobi方程的近似。自然的问题，我们在本文中解决的是如何这两个主题（减少和汉密尔顿-雅可比理论）适合在一起。我们得到了一个简化和重建过程的哈密顿-雅可比方程的对称性，甚至在广义的意义下澄清以下。几个应用程序和关系到其他减少的汉密尔顿-雅可比理论的最后一节的文件。值得注意的是，作为一个副产品，我们得到了一个推广的Ge-Marsden约化过程。令人惊讶的是，在文献中可用于求解Hamilton-Jacobi方程的经典ansatz也是我们框架的特殊实例。
Hamilton-Jacobi approach to Berezinian singular systems
在这项工作中，我们提出了一个正式的推广的Hamilton-Jacobi形式主义，最近开发的奇异系统，包括拉格朗日变量的Berezin代数的元素。我们推导了这类系统的Hamilton-Jacobi方程，分析了奇异情况，得到了作为全微分方程的运动方程，并研究了这类方程的可积性条件。一个例子是解决使用哈密顿-雅可比和狄拉克的哈密顿形式化和结果进行了比较。
The covariant Hamilton-Jacobi formulation of Maxwell's equations is derived from the first-order (Palatini-like) Lagrangian using the analysis of constraints within the De~Donder-Weyl covariant Hamiltonian formalism and the corresponding polysymplectic reduction.
Hamilton-Jacobi Diffieties
微分几何形式化了微分方程的概念。本文引入并研究了Hamilton-Jacobi微分。他们是有限维subdiffitues的一个给定的diffitues和出现发挥了特殊的作用，在场论版本的几何哈密顿-雅可比理论。
The Hamilton-Jacobi formalism is used to analyze the Weyl theory in the weak-field limit. The complete set of involutive Hamiltonians is obtained, which are classified into involutive and non-involutive. The counting of degrees of freedom is performed. Additionally, the generalized brackets and gauge symmetries are reported.
Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
我们使用一种称为汉密尔顿化的技术，将非完整系统转化为汉密尔顿系统，为Chaplygin系统（一类具有对称性的非完整力学系统）发展了汉密尔顿-雅可比理论。我们给出了一个几何帐户的哈密尔顿化，确定哈密尔顿化的必要条件和充分条件，并应用传统的哈密尔顿-雅可比理论的哈密尔顿化系统。我们表明，在一定的充分条件下，Hamilton化系统的Hamilton-Jacobi方程的解也解决了非完整的Hamilton-Jacobi方程与原Chaubergin系统。通过几个例子说明了结果。
The Quantum Effective Mass Hamilton-Jacobi Problem
本文研究了基于位置相关质量模型的量子哈密顿-雅可比理论.用两种具有不同奇异结构的有效质量函数来研究Morse势和Poschl-Teller势.利用留数法求出了量子有效质量- Hamilton Jacobi方程的解.进一步证明了Morse势和Poschl-Teller势的广义非厄米Swanson哈密顿量的本征态可以由Riccati方程得到，而不需要求解微分方程.
Geometric Hamilton-Jacobi Field Theory
本文简要地回顾了我关于如何将几何Hamilton-Jacobi理论推广到纤维丛上的高阶导数域论的建议。
In this paper, we develop a Hamilton-Jacobi theory for forced Hamiltonian and Lagrangian systems. We study the complete solutions, particularize for Rayleigh systems and present some examples. Additionally, we present a method for the reduction and reconstruction of the Hamilton-Jacobi problem for forced Hamiltonian systems with symmetry. Furthermore, we consider the reduction of the Hamilton-Jacobi problem for a Čaplygin system to the Hamilton-Jacobi problem for a forced Lagrangian system.
In this paper we propose a Hamilton-Jacobi theory for implicit contact Hamiltonian systems in two different ways. One is the understanding of implicit contact Hamiltonian dynamics as a Legendrian submanifold of the tangent contact space, and another is as a Lagrangian submanifold of a certain symplectic space embedded into the tangent contact space. In these two scenarios, we propose a Hamilton-Jacobi theory specifically derived with the aid of Herglotz Lagrangian dynamics generated by non-regular Lagrangian functions.
We develop the Hamilton-Jacobi formalism for Podolsky's electromagnetic theory on the null-plane. The main goal is to build the complete set of Hamiltonian generators of the system, as well as to study the canonical and gauge transformations of the theory.
Following the analysis we have presented in a previous paper (that we refer to as [I]), we describe a Noether theorem related to symmetries, with the associated reduction procedures, for classical dynamics within the Lagrangian and the Hamilton-Jacobi formalism.
The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transformations of the theory are found. We find from integrability conditions on the Hamilton-Jacobi Hamiltonians that the theory is reduced to a $BF$ field theory defined only in terms of self-dual (or anti-self-dual) variables; we identify the dynamical variables and the counting of physical degrees of freedom is performed. In addition, we compare our…
Quantum Hamilton-Jacobi Quantization and Shape Invariance
本文证明常规势的可加形状不变性与未破缺超对称性足以保证其在量子哈密顿-雅可比量子化框架中可解，从而扩展了该方法的适用范围。
The Hamilton-Jacobi Formalism for Higher Order Field Theories
本文将哈密顿力学的几何Hamilton-Jacobi形式推广到具有正则拉格朗日密度的高阶域论。我们还调查的依赖关系的形式主义的拉格朗日密度的类中产生相同的欧拉-拉格朗日方程。
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