616 research outputs found
Noether Symmetries and Critical Exponents
We show that all Lie point symmetries of various classes of nonlinear
differential equations involving critical nonlinearities are
variational/divergence symmetries.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
On the paper "Symmetry analysis of wave equation on sphere" by H. Azad and M. T. Mustafa
Using the scalar curvature of the product manifold S^{2}X R and the complete
group classification of nonlinear Poisson equation on (pseudo) Riemannian
manifolds, we extend the previous results on symmetry analysis of homogeneous
wave equation obtained by H. Azad and M. T. Mustafa [H. Azad and M. T. Mustafa,
Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl., 333 (2007)
1180--1888] to nonlinear Klein-Gordon equations on the two-dimensional sphere.Comment: Version accepted in J. Math. Anal. App
Conservations Laws for Critical Kohn-Laplace Equations on the Heisenberg Group
Using the complete group classification of semilinear differential equations
on the three-dimensional Heisenberg group carried out in a preceding work, we
establish the conservation laws for the critical Kohn-Laplace equations via the
Noether's Theorem.Comment: 9 pages, 1 table, submitted for publicatio
Special Conformal Groups of a Riemannian Manifold and Lie Point Symmetries of the Nonlinear Poisson Equation
We obtain a complete group classification of the Lie point symmetries of
nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using
this result we study their Noether symmetries and establish the respective
conservation laws. It is shown that the projection of the Lie point symmetries
on are special subgroups of the conformal group of M. In particular, if the
scalar curvature of M vanishes, the projection on M of the Lie point symmetry
group of the Poisson equation with critical nonlinearity is the conformal group
of the manifold. We illustrate our results by applying them to the Thurston
geometries.Comment: Paper submitted for publicatio
Pohozhaev and Morawetz Identities in Elastostatics and Elastodynamics
We construct identities of Pohozhaev type, in the context of elastostatics
and elastodynamics, by using the Noetherian approach. As an application, a
non-existence result for forced semi-linear isotropic and anisotropic elastic
systems is established
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