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Comparison of some Lie-symmetry-based integrators
Journal of Computational Physics, 2011 International audienceLie-symmetry based integrators are constructed in order to preserve the local invariance properties of the equations. The geometrical methods leading to discretized equations for numerical computations involve many different ...
Pierre Sagaut
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Lie Symmetries of Ishimori Equation
Communications in Theoretical Physics, 2013Summary: 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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Lie symmetries and superintegrability
Journal of Physics A: Mathematical and Theoretical, 2012We 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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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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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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Symmetries of Hamiltonian Systems on Lie Algebroids
Journal of Mathematical Sciences, 2023Lie algebroids are a generalization of tangent bundles and Lie algebras. Hamiltonian systems are introduced on Lie algebroids, and Jacobi endomorphisms and dynamical covariant derivatives allow to define infinitesimal symmetries and Noether theory on Lie algebroids.
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Related Evolution Equations and Lie Symmetries
SIAM Journal on Mathematical Analysis, 1985The 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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Deformation of Lie derivative and μ-symmetries
Journal of Physics A: Mathematical and Theoretical, 2007We 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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Lie symmetries and integrability
Physics Letters A, 1987Abstract 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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