Results 271 to 280 of about 33,448 (315)

Lie symmetries and superintegrability

Journal of Physics A: Mathematical and Theoretical, 2012
We show that a known superintegrable system in two-dimensional real Euclidean space (Post and Winternitz 2011 J. Phys. A: Math. Theor. 44 162001) can be transformed into a linear third-order equation: consequently we construct many autonomous integrals?polynomials up to order 18?for the same system.
M.C. Nucci, S. Post
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Lie Symmetries of Ishimori Equation

Communications in Theoretical Physics, 2013
Summary: The Ishimori equation is one of the most important (2+1)-dimensional integrable models, which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations. Based on the importance of Lie symmetries in analysis of differential equations, in this paper we derive Lie symmetries for the Ishimori
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Symmetry in Lie optics

Annals of Physics, 1986
Optical systems are investigated with respect to their symmetries. Special emphasis is paid to refracting surfaces, which have no strict equivalents in mechanics. The \({\mathfrak so}(3)\)-symmetry of a spherical surface is discussed which allows the recursive calculation of its aberration coefficients. Explicit results are given for coefficients up to
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Related Evolution Equations and Lie Symmetries

SIAM Journal on Mathematical Analysis, 1985
The problem of classification of evolution equations \[ (1)\quad v_ t=K(y^ 1,...,y^ n,v,\partial^{i_ 1+...+i_ n}v/\partial y^{i_ 1}...\partial y_ n^{i_ n}), \] where \(y_ 1,...,y_ n\) are space coordinates, with respect to transformations (2) \(t=t(s,x)\), \(y^ j=y^ j(s,x)\), \(v=v(s,x,u)\) is discussed. In general, the right- hand side of the equation
Kalnins, E. G., Miller, Willard jun.
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Lie symmetries and integrability

Physics Letters A, 1987
Abstract All two-dimensional time independent potentials admitting point Lie symmetries and Noether symmetries are presented here. Excluding the potentials admitting time translation and dilation symmetries only, they form a small subclass of the known integrable potentials.
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Lie symmetries of Hirota’s bilinear equations

Journal of Mathematical Physics, 1991
The existence of Lie-point symmetries for a family of partial differential equations (PDEs) written in Hirota’s bilinear formalism is investigated. These equations have been studied in previous publications from the point of view of the existence of multisoliton solutions and also of the Painlevé property and are either known as integrable or good ...
Tamizhmani, K. M., Ramani, A., Grammaticos, B.   +2 more
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Canonical Realizations of Lie Symmetry Groups

Journal of Mathematical Physics, 1966
A general theory of the realizations of Lie groups by means of canonical transformations in classical mechanics is given. The problem is the analog to that of the characterization of the projective representations in quantum mechanics considered by Wigner, Bargmann, and others in the case of the Galilei and the Lorentz group. However, no application to
Pauri, M., Prosperi, G. M.
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Lie Symmetry Group Methods

2013
This chapter introduces Lie Symmetry Group Methods as a powerful tool which can be used to algorithmitically solve partial differential equations. The latter feature prominently in mathematical finance, and we introduce Lie Symmetry methods by using them to algorithmitically solve the most famous partial differential equation in mathematical finance ...
Jan Baldeaux, Eckhard Platen
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Poincare normal forms and Lie point symmetries

Journal of Physics A: Mathematical and General, 1994
Summary: We study Poincaré normal forms of vector fields in the presence of symmetry under general -- i.e. not necessarily linear -- diffeomorphisms. We show that it is possible to reduce both the vector field and the symmetry diffeomorphism to normal form by means of an algorithmic procedure similar to the usual one for Poincaré normal forms without ...
CICOGNA, GIAMPAOLO, Gaeta G.
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