相关论文: Nonconcentration of energy for a semilinear Skyrme…
One of the most interesting open problems concerning the Skyrme model of nuclear physics is the regularity of its solutions. In this article, we study 2+1 dimensional equivariant Skyrme maps, for which we prove, using the method of…
We study a semi-linear version of the Skyrme system due to Adkins and Nappi. The objects in this system are maps from $(1+3)$-dimensional Minkowski space into the $3$-sphere and 1-forms on $\mathbb{R}^{1+3}$, coupled via a Lagrangian…
It is proved that the quantum-mechanical consideration of global breathing of a hedgehog-like field configuration leads to the dynamically stable soliton solutions in the nonlinear sigma-model without the Skyrme term. Such solutions exist…
An omega-meson extension of the Skyrme model - without the Skyrme term but including the pion mass - first considered by Adkins and Nappi is studied in detail for baryon numbers 1 to 8. The static problem is reformulated as a constrained…
Recent results suggest that multi-Skyrmions stabilized by omega mesons have very similar properties to those stabilized by the Skyrme term. In this paper we present the results of a detailed numerical investigation of a (2+1)-dimensional…
We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the…
We investigate a semilinear modification for the wave map problem proposed by Adkins and Nappi, and prove that in the equivariant case the solution remain continuous at the first possible singularity.
We study the asymptotic behaviour of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of…
The Maxwell--Chern--Simons model with scaler matter in the adjoint representation is analyzed from an alternative approach which is regular in the $\theta \to 0$ limit. This method is complementary to the usual operator formalism applied to…
We construct axially symmetric solutions of U(1) gauged Skyrme model. Possessing a nonvanishing magnetic moment, these solitons have also a nonzero angular momentum proportional to the electric charge.
Numerical methods are used to compute sphaleron solutions of the Skyrme model. These solutions have topological charge zero and are axially symmetric, consisting of an axial charge n Skyrmion and an axial charge -n antiSkyrmion (with n…
In this paper, we consider semilinear elliptic problems in a bounded domain $\Omega$ contained in a given unbounded Lipschitz domain $\mathcal C \subset \mathbb R^N$. Our aim is to study how the energy of a solution behaves with respect to…
We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy…
A systematic numerical study of the classical solutions to the combined system consisting of the Georgi-Glashow model and the SO(3) gauged Skyrme model is presented. The gauging of the Skyrme system permits a lower bound on the energy, so…
We find soliton solutions of the noncommutative Maxwell-Chern-Simons theory confined to a finite quantum Hall droplet. The solitons are exactly as hypothesized in \cite{Manu}. We also find new variations on these solitons. We compute their…
We show that the least energy conditions in the gauged nonlinear sigma model with Chern-Simons term lead to exact soliton-like solutions which have the same features as domain walls. We will derive and discuss the corresponding solutions,…
We consider systems of weakly coupled Schr\"odinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and…
This paper studies the concentration phenomena to nonlinear Schrodinger equations with magnetic potentials and constant electric potentials. We find that the magnetic field plays an important role in the location of concentrations if the…
For a domain $\Omega\subset\dR^N$ we consider the equation $ -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region…
In this paper, we study the semiclassical limit for the stationary magnetic nonlinear Schr\"odinger equation \begin{align}\label{eq:initialabstract}\left( i \hbar \nabla + A(x) \right)^2 u + V(x) u = |u|^{p-2} u, \quad x\in…