We study the existence and stability of ground state solutions or solitons to a nonlinear stationary equation on hyperbolic space. The method of concentration compactness applies and shows that the results correlate strongly to those of Euclidean space.

The strong instability of ground state standing wave solutions eφω(x) for nonlinear Klein-Gordon equations has been known only for the case ω = 0. In this paper we prove the strong instability for small frequency ω.

The paper gives a different proof for exitence of ground state solutions to the semilinear problem −∆u + u = b(x)up, p > 2, on RN , where b is invariant with respect to a free acting subgroup of O(N) with m elements. While the standard concentration compactness argument suggests the solvability condition inf b(x)/b∞ ≥ 1, symmetric ground state solutions exist whenever inf b(x)/b∞ > δm, where δm...

It has recently been argued that D-branes in bosonic string theory can be described as noncommutative solitons, outside whose core the tachyon is condensed to its ground state. We conjecture that, in addition, the local U(1) gauge symmetry is restored to a U(∞) symmetry in the vacuum outside this core. We present new solutions obeying this boundary condition. The tension of these solitons agree...

The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially we prove a number of lower and upper bounds for the resolvent of such operators. We consider two applications of these results. First we obtain pointwise estimates for principal eigenfunction of jump generators perturbed by a compactly supported potential (so-call...

We show that the “boundary crossing-unitarity equation” recently proposed by Ghoshal and Zamolodchikov is a consequence of the boundary bootstrap equation for the S-matrix and the wall-bootstrap equation. We solve this set of equations for all affine Toda theories related to simply laced Lie algebras, obtaining explicit formulas for the W-matrix which encodes the scattering of a particle with t...

We consider the following shadow system of the GiererMeinhardt system with saturation: ⎧⎪⎨ ⎪⎩ At = 2∆A−A+ A2 ξ(1+kA2) in Ω× (0,∞), τξt = −ξ + 1 |Ω| ∫ Ω A dx in (0,+∞), ∂A ∂ν = 0 on ∂Ω× (0,∞), where > 0 is a small parameter, τ ≥ 0, k > 0 and Ω ⊂ R is smooth bounded domain. The case k = 0 has been studied by many authors in recent years. Here we give some sufficient conditions on k for the existe...

Demagnetization, commonly employed to study ferromagnets, has been proposed as the basis for an optimization tool, a method to find the ground state of a disordered system. Here we present a detailed comparison between the ground state and the demagnetized state in the random field Ising model, combing exact results in d = 1 and numerical solutions in d = 3. We show that there are important dif...

We discuss the ground state and some excited states of the half-filled Hubbard model defined on an open chain with L sites, where onlyone of the boundary sites has a different value of chemical potential.We consider the case when the boundary site has a negative chemicalpotential −p and the Hubbard coupling U is positive. By an analyticmethod we show that when p is large...

In this article, we investigate the asymptotic behavior of positive ground state solutions, as α→∞, for the following Hénon type system −∆u = 2p p+ q |x|αup−1vq , −∆v = 2q p+ q |x|αupvq−1, in B1(0) with zero boundary condition, where B1(0) ⊂ RN (N ≥ 3) is the unit ball centered at the origin, p, q > 1, p+ q < 2∗ = 2N/(N − 2). We show that both components of the ground solution pair (u, v) conce...