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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
守恒量 两阶段物理信息 神经网络方法 局部波解
2023/5/5
With the advantages of fast calculating speed and high precision, the physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. B...
Non-Noether Symmetries and Lutzky Conserved Quantities for Mechanico-Electrical Systems
Mechanico-electrical system Non-Noether symmetry Lutzky conserved quantity
2012/8/7
We apply the non-Noether symmetry theory for mechanical systems to Lagrange–Maxwell mechanico-electrical systems. For these systems,
we derive the Lutzky conserved quantities from the corresponding e...
Conserved quantities and generalized solutions of the ultradiscrete KdV equation
Conserved quantities generalized solutions ultradiscrete KdV equation
2011/2/22
We construct generalized solutions to the ultradiscrete KdV equation,including the so-called negative solition solutions. The method is based on the ultradiscretization of soliton solutions to the dis...
On Symmetry and Conserved Quantities in Classical Mechanics
classical mechanics symmetry conserved quantities
2008/4/22
This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. T...
We construct and analyze a family of semi-discretized difference
schemes with two parameters for the Korteweg-de Vries (KdV) equation.
The scheme possesses the first four near-conserved quantities f...
In this paper, we present a new semi-discrete difference scheme for the KdV equation, which possesses the first four nearconserved quatities. The scheme is better than the past one given in [4], becau...
On Form Invariance, Lie Symmetry, and Three Kinds of Conserved
Quantities of Generalized Lagrange's Equations
form invariance Lie symmetry conserved quantity
generalized classical mechanics Lagrange's
equation
2007/8/15
2007Vol.48No.1pp.37-42DOI:
On Form Invariance, Lie Symmetry, and Three Kinds of Conserved
Quantities of Generalized Lagrange's Equations
ZHAO Shu-Hong1,2 and LIANG Li-Fu1
...
Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems
Vacco dynamical system Lie symmetry general Hojman
conserved quantity Lutzky conserved quantity
2007/8/15
2006Vol.46No.2pp.265-268DOI:
Lie Symmetry and Conserved Quantities for Nonholonomic Vacco Dynamical Systems
DING Ning and FANG Jian-Hui
College of Physics and Technology...
Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space
unified symmetry mechanical system conserved quantity phase space
2007/8/15
2006Vol.46No.1pp.97-100DOI:
Unified Symmetry and Conserved Quantities of Mechanical System in Phase Space
FANG Jian-Hui, DING Ning, and WANG Peng
College of Physics Sci...
Generalized Lutzky Conserved Quantities of Holonomic Systems with
Remainder Coordinates Subjected to Unilateral Constraints
analytical mechanics remainder coordinate unilateral
constraint holonomic system symmetry conserved quantity
2007/8/15
2006Vol.45No.4pp.732-736DOI:
Generalized Lutzky Conserved Quantities of Holonomic Systems with
Remainder Coordinates Subjected to Unilateral Constraints
ZHANG Yi
Departm...
Lie Symmetrical Non-Noether Conserved Quantities of
Poincarè-Chetaev Equations
Poincarè-Chetaev equations Lie symmetry non-Noether conserved quantity
2007/8/15
2005Vol.44No.2pp.223-225DOI:
Lie Symmetrical Non-Noether Conserved Quantities of
Poincarè-Chetaev Equations
ZHANG Peng-Yu and FANG Jian-Hui
College of Physics and Techn...