Related papers: Lie Point Symmetries and Commuting Flows for Equat…
A full symmetry classification is given for models of energy transport in radiant plasma when the mass density is spatially variable and the diffusivity is nonlinear. A systematic search for conservation laws also leads to some potential…
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
We present an exposition of a method of discretizing ordinary differential equations while preserving their Lie point symmetries. This method is very general and can be applied to any ODE with a nontrivial symmetry group. The method is…
A remarkable number of different numerical algorithms can be understood and analyzed using the concepts of symmetric spaces and Lie triple systems, which are well known in differential geometry from the study of spaces of constant curvature…
Lattice kinetic equations incorporating the effects of external/internal force fields via a shift of the local fields in the local equilibria, are placed within the framework of continuum kinetic theory. The mathematical treatment reveals…
An alternative method of constructing the formal diagonalization for the discrete Lax operators is proposed which can be used to calculate conservation laws and in some cases generalized symmetries for discrete dynamical systems. Discrete…
The classification of the Lie point symmetries of the nonlinear filtration equation gives the generic case and three special cases. By restricting to a special class of functions, we show that the Lie symmetries of the nonlinear filtration…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable…
We study the underlying nonlinear partial differential equation that governs the behaviour of spherically symmetric charged fluids in general relativity. We investigate the conditions for the equation to admit a first integral or be reduced…
A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second order geometry and Ito integration on manifolds, allows us to give a natural and effective…
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
We use "generalized" version of total variation, coarea formulas, isoperimetric inequalities to obtain sharp estimates for solutions (and for their gradients) to anisotropic elliptic equations with a lower order term, comparing them with…
We carry out the group classification of the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The equivalence group of this class is found by the…
We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…
The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries…
We develop the approach to the problem of integrable discretization based on the notion of $r$--matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems with the Lax matrices of the underlying…
We propose an improvement of the differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method our technique yields positive pressure for all temperatures…
In the present work we find the Lie point symmetries of the Ricci flow on an $n$-dimensional manifold. and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics. We apply this…