Journal ArticleDOI
An operator approach to Poisson brackets
TLDR
In this article, a general approach to Poisson brackets, based on the study of the Lie algebra of potential operators with respect to closed skew-symmetric bilinear forms, is proposed.About:
This article is published in Annals of Physics.The article was published on 1976-07-01. It has received 25 citations till now. The article focuses on the topics: Poisson bracket & Poisson algebra.read more
Citations
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Journal ArticleDOI
A Simple model of the integrable Hamiltonian equation
TL;DR: In this paper, a method of analysis of the infinite-dimensional Hamiltonian equations which avoids the introduction of the Backlund transformation or the use of the Lax equation is suggested, based on the possibility of connecting in several ways the conservation laws of special Hamiltonian equation with their symmetries by using symplectic operators.
Book ChapterDOI
A geometrical approach to the nonlinear solvable equations
TL;DR: In this paper, a geometrical approach to the nonlinear solvable equations, based on the study of the "groups of motion" of special infinite-dimensional manifolds called "symplectic Kahler manifolds", is suggested.
Journal ArticleDOI
Oriented attachment induces fivefold twins by forming and decomposing high-energy grain boundaries
TL;DR: Step-by-step mechanisms for forming fivefold twinned nanoparticles are demonstrated in gold, platinum, and palladium nanoparticles and provide guidance for controlling twin structures and morphologies across a wide range of materials.
Journal ArticleDOI
A fully symmetric nonlinear biorthogonal decomposition theory for random fields
TL;DR: In this paper, the authors present a general approach for nonlinear biorthogonal decomposition of random fields based on a fully symmetric operator framework that unifies different types of expansions and allows for a simple formulation of necessary and sufficient conditions for their completeness.
Journal ArticleDOI
Integrable properties of the differential-difference Kadomtsev-Petviashvili hierarchy and continuum limits
TL;DR: In this paper, the authors reveal clear links between the differential-difference Kadomtsev-Petviashvili hierarchy and the (continuous) Lie algebras, together with their symmetries, Hamiltonian structures and conserved quantities.
References
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Book
Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Book
Foundations of mechanics
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.