The Cauchy problem for the 2D Boussinesq system with periodic boundary conditions is studied. The global existence and uniqueness of a solution with initial data (u(0), θ(0)) ∈ Φ(α) is established, where Φ(α) is the space of functions the kth Fourier coefficients of which decay at infinity as 1 |k|α , α > 2. It is proved that the solution becomes analytic at any positive time. Bibliography: 10 ...

We consider the one-dimensional Willmore equation subject to Navier boundary conditions, i.e. the position and the curvature are prescribed on the boundary. In a previous work, explicit symmetric solutions to symmetric data have been constructed. Within a certain range of boundary curvatures one has precisely two symmetric solutions while for boundary curvatures outside the closure of this rang...

We have simulated a system of classical particles confined on the surface of a sphere interacting with a repulsive r potential. The same system simulated on a plane with periodic boundary conditions has van der Waals loops in pressure-density plots which are usually interpreted as evidence for a first order melting transition, but on the sphere such loops are absent. We also investigated the st...

The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanni...

No abstract. Erratum After publication of the original article [1] it came to the Publisher's attention that the first author's name had been listed incorrectly. The list of authors has now been corrected. We apologise for any inconvenience this has caused. which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can exponentially grow with time under the same conditions as for the massless case. The proofs are based on estimates of exactly given mass-induced corrections...

x(n + 1) : x(n)exp Jr (n ) (1 x(n) K(n) ] J ' where {r(n)} and {K(n)} are positive w-periodic sequences. Sufficient conditions are obtained for the existence of a positive and globally asymptotically stable w-periodic solution. Counterexamples are given to illustrate that the conclusions in [1] are incorrect. (~) 2003 Elsevier Science Ltd. All rights reserved.

We propose the exact boundary S matrix for breathers of theN = 2 supersymmetric sine-Gordon model. We argue that this S matrix has three independent parameters, in agreement with a recently-proposed action. We also show, contrary to a previous claim, that the “universal” supersymmetric boundary S matrix commutes with two supersymmetry charges. General N = 2 supersymmetric boundary integrable mo...

In the context of coupled periodic waveguides, “couplonics” refers to the rigorous equivalence between continuous wave coupling and localized interactions. We extend it here to a cyclic ternary system, looked upon as the simplest discrete photonic crystal with actual periodic boundary conditions. A linear decomposition on a supermode basis enables one to reduce the original six-wave problem to ...