Results 241 to 250 of about 437,825 (261)

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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Lie symmetries and reductions

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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Deformation of Lie derivative and μ-symmetries

Journal of Physics A: Mathematical and Theoretical, 2007
We introduce, in the spirit of Witten's gauging of exterior differential, a deformed Lie derivative that allows a geometrical interpretation of λ- and μ-symmetries, in complete analogy with standard symmetries. The case of variational symmetries (both for ODEs and for PDEs) is also considered in this approach, leading to λ- and μ-conservation laws.
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Conservation laws and Lie-B�cklund symmetry

Russian Physics Journal, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Lie-point symmetries in bifurcation problems

1992
The authors develop a theory of bifurcations of differential equations with Lie point symmetries. Viewing the differential equation as an ``algebraic equation'' on some jet bundle is the key of the analysis. The authors show how the well-known results of equivariant bifurcation theory can be formulated in this context and how the results carry over ...
CICOGNA, GIAMPAOLO, Gaeta G.
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