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Instability induced by symmetry reduction
Physical Review Letters, 1992Summary: We demonstrate that instabilities in a Hamiltonian system can occur via deformations that reduce the symmetry of the system. The movement of eigenvalues at an equilibrium point of a family of Hamiltonian systems is constrained by the symmetry type of the system.
Guckenheimer, J., Mahalov, A.
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VARIATIONAL CALCULUS, SYMMETRIES AND REDUCTION
International Journal of Geometric Methods in Modern Physics, 2006Variational Principles and Symmetries are both fundamental ingredients of the most relevant (either classical or modern) physical theories, and of many interesting models in Pure and Applied Mathematics. While the variational principle determines the law (differential and sometimes algebraic equations) of the dynamics, the symmetries give way to ...
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Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation
Communications in Theoretical Physics, 2017Summary: The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries.
Wu, Jian-Wen, Lou, Sen-Yue, Yu, Jun
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Symmetry Reductions of the Skyrme-Faddeev Model
Acta Applicandae Mathematicae, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
MARTINA, Luigi, G. I. Martone, S. Zykov
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Reduction of Network States Under Symmetries
Bell System Technical Journal, 1978It is a folk-theorem of traffic theory that if all sources have the same stochastic behavior, then symmetries of a telephone connecting network can be used to lump together equivalent states and to reduce the number of equations to be solved for the state probabilities.
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REDUCTION OF DIFFERENTIAL EQUATIONS WITH SYMMETRIES
Mathematics of the USSR-Izvestiya, 1981A method for constructing group-invariant solutions of differential equations is described. At the foundation of the method lies a reduction of the dimension of the base of a bundle of -jets of functions by means of a passage to the manifolds of orbits of the contact action of the Lie group of partial symmetries of the differential equation.
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Symmetry Reduction From Interactions to Particles
International Journal of Theoretical Physics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2009
Abstract Phrases like ‘the unifying role of symmetry in . . . ‘ feature prominently in the popular science literature. Depending on the subject, the symmetry may be ‘cosmic’, ‘Platonic’, ‘perfect’, ‘broken’, or even ‘super’.
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Abstract Phrases like ‘the unifying role of symmetry in . . . ‘ feature prominently in the popular science literature. Depending on the subject, the symmetry may be ‘cosmic’, ‘Platonic’, ‘perfect’, ‘broken’, or even ‘super’.
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Group actions, symmetries and reduction
2009Abstract An action of a group on a set is a map that associates to each element of the group an invertible transformation of the given set, in such a way that the group operation corresponds to composition of transformations. Thus, the group may be thought of as a group of transformations.
Darryl D Holm +3 more
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Direct Method of Symmetry Reductions. Weak Symmetries
2021Andrei D. Polyanin, Alexei I. Zhurov
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