On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs

Monica Ugaglia

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On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs

机译：演化PDEs的时变约简的哈密顿和拉格朗日结构

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In this paper we study the reductions of evolutionary PDEs on the manifold of the stationary points of time-dependent symmetries. In particular we describe how that the finite-dimensional Hamiltonian structure of the reduced system is obtained from the Hamiltonian structure of the initial PDE and we construct the time-dependent Hamiltonian function. We also present a very general Lagrangian formulation of the procedure of reduction. As an application we consider the case of the Painleve equations PI, PII, PIII, PVI and also certain higher order systems appeared in the theory of Frobenius manifolds.

机译：在本文中，我们研究了随时间变化的对称平稳点的流形上演化PDE的减少。特别是，我们描述了如何从初始PDE的哈密顿结构中获得简化系统的有限维哈密顿结构，并构造时间相关的哈密顿函数。我们还介绍了还原过程的非常一般的拉格朗日公式。作为一种应用，我们考虑了Painleve方程PI，PII，PIII，PVI的情况，以及某些高阶系统出现在Frobenius流形理论中。

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《Differential geometry and its applications》 |2002年第1期|共33页
作者
Monica Ugaglia;
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正文语种 eng
中图分类微分几何;
关键词
Painleve equations; integrable systems; scaling symmetries;

机译：Painleve方程;可积系统;尺度对称;

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专利

1. On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs [J] . Monica Ugaglia Differential geometry and its applications . 2002,第1期

机译：演化PDEs的时变约简的哈密顿和拉格朗日结构
2. On properties of hamiltonian structures for a class of evolutionary PDEs [J] . Liu SQ, Wu CZ, Zhang YJ Letters in Mathematical Physics: A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics . 2008,第1期

机译：关于一类演化PDEs的哈密尔顿结构的性质
3. ARBITRARY LAGRANGIAN EULERIAN-TYPE FINITE ELEMENT METHODS FORMULATION FOR PDEs ON TIME-DEPENDENT DOMAINS WITH VANISHING DISCRETE SPACE CONSERVATION LAW [J] . Ivancic Filip, Sheu Tony W-H, Solovchuk Maxim SIAM Journal on Scientific Computing . 2019,第3期

机译：任意拉格朗日Eulerian型有限元方法在消失离散空间守恒法中对时间依赖域的PDE
4. Computation of empirical eigenfunctions and order reduction for control of time-dependent parabolic PDEs [C] . Armaou, A., Dubljevic, . 2003

机译：经验本征函数的计算和降阶，以控制时间相关的抛物线型偏微分方程
5. Establishing the Viability and Efficacy of in Situ Reduction via Lagrangian Representations for Time-Dependent Vector Fields [D] . ?Sane, Sudhanshu 2020

机译：通过拉格朗日表示对时间依赖的矢量领域的原位减少的可行性和功效
6. Evolutionary Differences in Glycosaminoglycan Fine Structure Detected by Quantitative Glycan Reductive Isotope Labeling [O] . Roger Lawrence, Sara K. Olson, Robert E. Steele, 2008

机译：糖胺聚糖精细结构的进化差异检测。定量糖还原同位素贴标
7. On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs [O] . Ugaglia Monica 2002

机译：演化PDEs的时变约简的哈密顿和拉格朗日结构
8. Integrable 2+1 Dimensional Equations, Their Recursion Operators and Bi-Hamiltonian Structures as Reduction of Multidimensional Systems [R] . Santini, P. M. 1987

机译：可积2 + 1维方程，它们的递归算子和双哈密顿结构作为多维系统的约简

On the Hamiltonian and Lagrangian structures of time-dependent reductions of evolutionary PDEs

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