2,964 research outputs found
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
Differential Invariants of Conformal and Projective Surfaces
We show that, for both the conformal and projective groups, all the
differential invariants of a generic surface in three-dimensional space can be
written as combinations of the invariant derivatives of a single differential
invariant. The proof is based on the equivariant method of moving frames.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Classical and nonclassical symmetries of a generalized Boussinesq equation
We apply the Lie-group formalism and the nonclassical method due to Bluman
and Cole to deduce symmetries of the generalized Boussinesq equation, which has
the classical Boussinesq equation as an special case. We study the class of
functions for which this equation admit either the classical or the
nonclassical method. The reductions obtained are derived. Some new exact
solutions can be derived
Stokes phenomenon and matched asymptotic expansions
This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions
On the variational noncommutative Poisson geometry
We outline the notions and concepts of the calculus of variational
multivectors within the Poisson formalism over the spaces of infinite jets of
mappings from commutative (non)graded smooth manifolds to the factors of
noncommutative associative algebras over the equivalence under cyclic
permutations of the letters in the associative words. We state the basic
properties of the variational Schouten bracket and derive an interesting
criterion for (non)commutative differential operators to be Hamiltonian (and
thus determine the (non)commutative Poisson structures). We place the
noncommutative jet-bundle construction at hand in the context of the quantum
string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries'
(July 18-23, 2011; JINR Dubna, Russia), 4 page
On the Structure of Lie Pseudo-Groups
We compare and contrast two approaches to the structure theory for Lie
pseudo-groups, the first due to Cartan, and the second due to the first two
authors. We argue that the latter approach offers certain advantages from both
a theoretical and practical standpoint
An integrable shallow water equation with peaked solitons
We derive a new completely integrable dispersive shallow water equation that
is biHamiltonian and thus possesses an infinite number of conservation laws in
involution. The equation is obtained by using an asymptotic expansion directly
in the Hamiltonian for Euler's equations in the shallow water regime. The
soliton solution for this equation has a limiting form that has a discontinuity
in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques
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