Related papers: A Physical Approach to Polya's Conjecture
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless…
"Fluid polyamorphism" is the existence of different condensed amorphous states in a single-component fluid. It is either found or predicted, usually at extreme conditions, for a broad group of very different substances, including helium,…
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
In this paper, we develop a new index theory for manifolds with polyhedral boundary. As an application, we prove Gromov's dihedral extremality conjecture regarding comparisons of scalar curvatures, mean curvatures and dihedral angles…
The paper is of scientific-methodical character. The classical soap film shape (minimal surface) problem is considered, the film being stretched between two parallel coaxial rings. An analytical approach based on relations to the…
This paper investigates the weakly nonlinear isotropic bi-directional Benney--Luke (BL) equation, which is used to describe oceanic surface and internal waves in shallow water, with a particular focus on soliton dynamics. Using the Whitham…
Plane waves are regarded as the general solution of the wave equation. However the plane wave expansion of standing waves by means of complex phasors leads to a theory in which the time coordinate does not receive the same treatment as the…
The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in arithmetic geometry and singularity theory. Even the…
Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser…
We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.
Test particles interact with a medium by means of a bimolecular reversible chemical reaction. Two species are assumed to be much more numerous so that they are distributed according fixed distributions: Maxwellians and Dirac's deltas.…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.
We describe direct imaging measurements of a colloidal sphere's diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
We study the variational equations for solitons in noncommutative scalar field theories in an even number of spatial dimensions. We prove the existence of spherically symmetric solutions for a sufficiently large noncommutativity parameter…
Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…