نتایج جستجو برای: lie symmetry method
تعداد نتایج: 1743648 فیلتر نتایج به سال:
We investigate Lie symmetries of Einstein’s vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on Einstein’s equations. Instead of setting to zero the coefficients of all independent partial derivatives (which involves a very complicated substitution of Einstei...
We apply nonlocal symmetry-like operators to systems of two first and two second-order ordinary differential equations to seek reduction to quadratures. The reduction of order of such systems is carried out with the help of analytic continuation of scalar equations in the complex plane. Examples are taken from the literature. Precisely it is shown how the reduction to quadratures of a system of...
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including those of the non-Lie type. An explicit example is made of the Dirac equation were we use our construction to find a class of conservation laws associated wi...
The nonlocal symmetry of the Drinfeld–Sokolov–Satsuma–Hirota system is obtained from the known Lax pair, and infinitely many nonlocal symmetries are given by introducing the internal parameters. Then the nonlocal symmetry is localized to a prolonged system by introducing suitable auxiliary dependent variables. By applying the classical Lie symmetry method to this prolonged system, two main resu...
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including those of the non-Lie type. An explicit example is made of the Dirac equation were we use our construction to find a class of conservation laws associated wi...
Lie group analysis is a powerful tool for obtaining exact similarity solutions of nonlinear (integro-) differential equations. In order to calculate the group-invariant solutions one first has to find the full Lie point symmetry group admitted by the given (integro-)differential equations and to determine all the subgroups of this Lie group. An effective, systematic means to classify the simila...
Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape invariance symmetry. Using this symmetry we have obtained their eigenspectrum. In the mean time we show equivalence of shape invariance symmetry and Lie algebraic symmetry...
Lie group analysis of the photo-induced fluorescence of Drosophila oogenesis with the asymmetrically localized Gurken protein has been performed systematically to assess the roles of ligand-receptor complexes in follicle cells. The (2×2) matrix representations resulting from the polarized tissue spectra were employed to characterize the asymmetrical Gurken distributions. It was found that the f...
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