Related papers: Splitting solitons on a torus
We study by numerical methods a particular kind of SU(N) Yang-Mills solutions of the Euclidean equations of motion which appear on the torus when twisted boundary conditions are imposed. These are instanton-like configurations with the…
In the study of holomorphic functions of one complex variable, one well-known theory is that of elliptic functions and it is possible to take the zeta-function of Weierstrass as a building stone of this vast theory. We are working the…
Topologically nontrivial states, the solitons, emerge as elementary excitations in 1D electronic systems. In a quasi 1D material the topological requirements originate the spin- or charge- roton like excitations with charge- or spin- kinks…
We investigate the interaction between two flat-top solitons within the cubic-quintic nonlinear Schr\"odinger equation framework. Our study results point towards a significant departure of flat-top solitons collisional characteristics from…
The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in…
A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological…
We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…
It is argued that the dynamics of the elastic scattering of high-energy protons at intermediate transferred momenta changes with the energy increase. It evolves from the multiple scattering at the external layer for energies about 10 GeV to…
A motion of point vortices with periodic boundary conditions is studied by using Weierstrass zeta functions. Scattering and recoupling of a vortex pair by a third vortex becomes remarkable when the vortex density is large. Clustering of…
We show that when a Chern-Simons term is added to the action of $SU(N)$ ($N\geq 3$) Yang-Mills theory in 5 dimensions the usual self-dual topological solitons present in the theory necessarily pick up a (topological) electric charge.
This paper is dedicated to studying various aspects of topological defects, appearing in mean-field theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We start by investigating topological charge…
In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the…
A new range of uniform $L^p$ resolvent estimates is obtained in the setting of the flat torus, improving previous results of Bourgain, Shao, Sogge and Yao. The arguments rely on the $\ell^2$-decoupling theorem and multidimensional Weyl sum…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
We study topological properties of automorphisms of 4-dimensional torus generated by integer symplectic matrices. The main classifying element is the structure of the topology of a foliation generated by unstable leaves of the automorphism.…
We identify and investigate the new parameter regime of small charge solitons in one-dimensional arrays of Josephson junctions. We obtain the dispersion relation of the soliton and show that it unexpectedly flattens in the outer region of…
Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of…
Under suitable conditions a flow on a torus $C^{(p)}$--close, with $p$ large enough, to a quasi periodic diophantine rotation is shown to be conjugated to the quasi periodic rotation by a map that is analytic in the perturbation size. This…
Systems whose potential energies consists of pieces that scale as r^-2 together with pieces that scale as r^2, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude for ever. Despite this pulsation these…
We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure…