Pages: 1 - 6
In two previous papers the quantization was discussed of three one-degree-of-freedom
Hamiltonians featuring a constant c, the value of which does not influence at all the
corresponding classical dynamics (which is characterized by isochronous solutions,
all of them periodic with period 2: "nonlinear...
Pages: 7 - 12
At the quantum level of a bidimensional conformal model, the conformal symmtry is broken by the diffeomorphism anomaly and the conformal covariance is not
maintained. Here we interpret geometrically this conformal covariance as an exact holomorphy condition on a two-dimensional Riemann surface on which...
Pages: 13 - 20
The classical reduction of order for scalar ordinary differential equations (ODEs) fails
for a system of ODEs. We prove a constructive result for the reduction of order for a
system of ODEs that admits a solvable Lie algebra of point symmetries. Applications
are given for the case of a system of two...
Pages: 21 - 46
A new approach to the finite-gap property for the Heun equation is constructed. The
relationship between the finite-dimensional invariant space and the spectral curve is
clarified. The monodromies are calculated and are expressed as hyperelliptic integrals.
Applications to the spectral problem for...
Pages: 47 - 74
We present a version of the conditional symmetry method in order to obtain multiple
wave solutions expressed in terms of Riemann invariants. We construct an abelian
distribution of vector fields which are symmetries of the original system of PDEs
subjected to certain first order differential constraints....
Pages: 75 - 101
Conditions necessary for the existence of local higher order generalized symmetries and
conservation laws are derived for a class of dynamical lattice equations with explicit
dependence on the spatial discrete variable and on time. We explain how to use the
obtained conditions for checking a given...
Pages: 102 - 112
The (Hamiltonian, rotation- and translation-invariant) "goldfish" N-body problem in
the plane is characterized by the Newtonian equations of motion
¨zn - i zn = 2
an,m zn zm (zn - zm)
written here in their complex version, entailing the identification of the real "physical"
Pages: 113 - 122
We consider the general properties of the replicator dynamical system from the stanpoint of its evolution and stability. Vector field analysis as well as spectral properties
of such system has been studied. A Lyaponuv function for the investigation of the
evolution of the system has been proposed....
Pages: 123 - 133
We examine the classical model of two competing species for integrability in terms
of analytic functions by means of the Painlevé analysis. We find that the governing
equations are integrable for certain values of the essential parameters of the system.
We find that, for all integrable cases with...
Pages: 134 - 140
A two-phase free boundary problem associated with nonlinear heat conduction is cosidered. The problem is mapped into two one-phase moving boundary problems for
the linear heat equation, connected through a constraint on the relative motion of
their moving boundaries. Existence and uniqueness of the...