相关论文: Weierstrass P-lumps
New CP1-soliton behaviour on a flat torus is reported. Defined by the Weierstrass elliptic function and numerically-evolved from rest, each soliton splits up in two lumps which eventually reunite, divide and get back together again, etc..…
Head-on collisions between two solitons in the pure $CP^1$ model on a flat torus are investigated via numerical simulations. The charge-two lumps, written out in terms of Weierstrass' elliptic $\wp$-function, are found to scatter at…
The slow dynamics of topological solitons in the CP^1 sigma-model, known as lumps, can be approximated by the geodesic flow of the L^2 metric on certain moduli spaces of holomorphic maps. In the present work, we consider the dynamics of…
Using numerical simulations, the stability and scattering properties of the O(3) model on a two-dimensional torus are studied. Its solitons are found to be unstable but can be stabilized by the addition of a Skyrme term to the Lagrangian.…
We study stationary rotating topological solitons in (2+1)-dimensional ${\mathbb C}P^2$ non-linear sigma model with a stabilizing potential term. We find families of $U(1)\times U(1)$ symmetric solutions with topological degrees larger than…
Reflection of wave packets from downward potential steps and attractive potentials, known as a quantum reflection, has been explored for bright matter-wave solitons with the main emphasis on the possibility to trap them on top of a…
The vacuum energy of two CP(1) solitons on a torus is computed numerically. A numerical technique for zeta-function regularisation is proposed to remove the divergences of the vacuum energy. After performing the numerical regularisation, we…
We report on the experimental observation of solitons propagating along a torus of fluid. We show that such a periodic system leads to significant differences compared to the classical plane geometry. In particular, we highlight the…
We study the scattering of lumps in the 2+1-dimensional Ising CFT, indirectly, by analytically continuing its spectrum using the Lorentzian inversion formula. We find evidence that the intercept of the model is below unity: $j_*\approx…
We consider the generalized dual transformation for elliptic/hyperelliptic $\wp$ functions up to genus three. For the genus one case, from the algebraic addition formula, we deduce that the Weierstrass $\wp$ function has the SO(2,1) $\cong$…
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
We introduce a two dimensional model for the Bose-Einstein condensate with both attractive and repulsive nonlinearities. We assume a combination of a double well potential in one direction, and an optical lattice along the perpendicular…
We consider the dynamics of two interacting lumps/solitons in a noncommutative gauge model. We show that equations of motion describing this dynamics can be reduced to ones of a two-dimensional mechanical system which is well studied and…
In the previous work (J. Geom. Phys. {\bf{39}} (2001) 50-61), the closed loop solitons in a plane, \it i.e., loops whose curvatures obey the modified Korteweg-de Vries equations, were investigated for the case related to algebraic curves…
We report the first experimental observation of vector surface solitons, which form at the edge and in the corner of two-dimensional laser-written waveguide arrays. These elliptically polarized vector states are composed of two orthogonally…
A class of exact solutions of the Skyrme model are obtained. They are described by the Weierstrass $\wp$-function or the Jacobi elliptic function. They are not solitonic but of wave character. They supply us with examples of the…
We study doubly periodic Bogomol'nyi-Prasad-Sommerfield (BPS) lumps in supersymmetric CP^{N-1} non-linear sigma models on a torus T^2. Following the philosophy of the Harrington-Shepard construction of calorons in Yang-Mills theory, we…
We introduce a two-dimensional (2D) system, which can be implemented in dual-core planar optical couplers with the Kerr nonlinearity in its cores, making it possible to blend effects of the PT symmetry, represented by the balanced linear…
Recently, the ZEUS collaboration has reported on several remarkable properties of events with a large rapidity gap in deep inelastic scattering. We suggest that the mechanism underlying these events is the scattering of electrons off lumps…
With the help of numerical simulations we study N-soliton scattering (N=3,4) in the (2+1)-dimensional CP^1 model with periodic boundary conditions. When the solitons are scattered from symmetrical configurations the scattering angles…