In this paper we prove existence of multiple-front solutions in a class of coupled reaction-diiusion equations with a small parameter. By a travelling wave Ansatz we reduce the problem to a four-dimensional system of ordinary diierential equations and prove existence of a large variety of n-jump homoclinic and heteroclinic solutions, n = 1; 2; 3; : : : using geometric singular perturbation theo...

Four-point functions of gauge-invariant operators in D = 4, N = 4 supersymmetric Yang-Mills theory are studied using N = 2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar two loop integral. The leading singular behaviour is obtained in the limit that two of the points approach one another. We find logarithmic singularities...

Inhibition in oscillatory networks of neurons can have apparently paradoxical e ects, sometimes creating dispersion of phases, sometimes fostering synchrony in the network. We analyze a pair of biophysically modeled neurons and show how the rates of onset and decay of inhibition interact with the time scales of the intrinsic oscillators to determine when stable synchrony is possible. We show th...

In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to e A = D 1AD2 and how singular values of a (nonsquare) matrix B change when it is perturbed to e B = D 1BD2, where D1 and D2 are assumed to be close to unitary matrices of suitable dimensions. We have been able to generalize many well-known perturbation theorems, including Ho man-Wielandt theorem and Weyl-Lid...

in this paper, we investigate a singular perturbation problem including a fourth order o.d.e. with general linear boundary conditions. firstly, we obtain the necessary conditions of solution of o.d.e. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

Duality symmetries for strings moving in non-trivial spacetime backgrounds are analysed. It is shown that, for backgrounds generated from compact WZW and coset models, such duality symmetries are exact to all orders in string perturbation theory. A global treatment of duality symmetries is given, by associating them to the known symmetries of affine current algebras ( affine-Weyl group and exte...

Duality symmetries for strings moving in non-trivial spacetime backgrounds are analysed. It is shown that for backgrounds generated from WZW and coset CFT models such duality symmetries are exact to all orders in string perturbation theory. Their implications for string dynamics in non-trivial/singular spacetimes are discussed. CERN-TH.7003/93 September 1993 ∗ Talk given at the EPS 93 Conferenc...

This paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. The work done in this area during the periods 1984–2000 and 2000–2005 has already been surveyed in 2002 and 2007 but our main objective is to produce a collection of important research articles of physical significance. In this paper, ...

A metapopulation model with explicit local dynamics is studied. Unlike many patch-based metapopulation models which assume that the local population within each patch is at its equilibrium, our model incorporates population changes in local patches that interact with metapopulation dynamics. The model keeps track of the fractions of patches that have species 1 only, species 2 only, or both spec...

A travelling waves analysis for a polyatomic gas with n internal energy storage modes is performed. In both the frozen ow and the equilibrium limit the existence and the qualitative behaviour of travelling waves are investigated. Methods from geometric singular perturbation theory are used to study these limits.