相关论文: Scalar Multi-Solitons on the Fuzzy Sphere

We first show that the effective non-relativistic theory of gravitationally interacting, massive integer-spin fields (spin-$0$, $1$, and $2$ in particular) is described by a $2s+1$ component Schr\"{o}dinger-Poisson action, where $s$ is the…

In both the Gardner equation and its extensions, the non-convex convection bounds the range of solitons / compactons velocities beyond which they dissolve and kink/anti-kink form. Close to solitons barrier we unfold a narrow strip of…

In this paper, we study the moduli space of Higgs pairs, which can be considered as a generalization of holomorphic pairs. Higgs pairs are an example of quiver bundles. We introduce the notion of $\tau$-stability of Higgs pairs for…

We study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the…

A new modulus of smoothness based on the Euler angles is introduced on the unit sphere and is shown to satisfy all the usual characteristic properties of moduli of smoothness, including direct and inverse theorem for the best approximation…

We describe a broad class of multi-field inflationary models with spontaneously broken conformal invariance. It generalizes the recently discovered class of cosmological attractors with a single inflaton field. In the new multi-field…

Complete, conformally flat metrics of constant positive scalar curvature on the complement of $k$ points in the $n$-sphere, $k \ge 2$, $n \ge 3$, were constructed by R\. Schoen [S2]. We consider the problem of determining the moduli space…

We study soliton solutions in scalar field theory with a variety of unbounded potentials. A subset of these potentials have Gaussian lump solutions and their fluctuation spectrum is governed by the harmonic oscillator problem. These lumps…

We derive an explicit expression for an associative star product on non-commutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This…

The main result of this paper is the explicit computation of the equations defining the moduli space of triples $(C,p,z)$ (where $C$ is an integral and complete algebraic curve, $p$ a smooth rational point and $z$ a formal trivialization…

We study the moduli space of solutions to the Seiberg-Witten equations with $N$ spinors on a compact Riemann surface. These moduli spaces arise in a program to define a new enumerative invariant of 3-manifolds. They are also of independent…

The moduli space of principally polarized abelian varieties with real structure and with level $N=4m$ structure (with $m \ge 1$) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over $\mathbb…

We investigate the geometry of the moduli space of N-vortices on line bundles over a closed Riemann surface of genus g > 1, in the little explored situation where 1 =< N < g. In the regime where the area of the surface is just large enough…

We consider the self-dual vortex equations on a positive line bundle L --> M over a compact Kaehler manifold of arbitrary dimension. When M is simply connected, the moduli space of vortex solutions is a projective space. When M is an…

In this paper we present soliton solutions of two coupled nonlinear Schodinger equations modulated in the bspace and time. The approach allows us to obatin solitons with large variety of solutions depending on the nonlinearity and the…

We consider the moduli space $\mathfrak{M}_{g,n}$ of Riemann surfaces of genus $g\ge0$ with $n\ge1$ ordered and directed marked points. For $d\ge 2g+n-1$ we show that $\mathfrak{M}_{g,n}$ is homotopy equivalent to a component of the…

In this article, we study kink soliton configurations in interacting scalar field theories containing two fields without $SO(2)$ invariance. We study a class of such theories, the well-known Montonen-Sarker-Trullinger-Bishop model is one of…

Using the Jacobi Elliptic Functions, an analytical solution is developed for the nonlinear amplitude equation of Surface Plasmon Polaritons (SPPs) in a graphene-dielectric waveguide. It is shown that the field localization of SPPs coupled…

We address the properties of two-dimensional surface solitons supported by the interface of a waveguide array whose nonlinearity is periodically modulated. When the nonlinearity strength reaches its minima at the points where the linear…

A strongly reflective modular form with respect to an orthogonal group of signature (2,n) determines a Lorentzian Kac--Moody algebra. We find a new geometric application of such modular forms: we prove that if the weight is larger than n…