We present a method to compute enclosures of the local invariant manifolds of a hyperbolic saddle of an analytic vector eld. By considering parametrisations of the invariant manifolds, instead of describing them as graphs of functions from the corresponding tangent spaces, we nd simple recursive formulae for their Taylor coe cients. In addition to this, we obtain rigorous bounds on the remainde...

Propagation of a Brillouin precursor in a Lorentz dispersive medium is considered. The precursor is excited by a sine modulated initial signal, with its envelope described by a hyperbolic tangent function. The purpose of the paper is to show how the rate of growth of the initial signal affects the form of the Brillouin precursor. Uniform asymptotic approach, pertinent to coalescing saddle point...

A well-known conjecture in mathematical physics asserts that the interacting Bose gas exhibits Bose-Einstein condensation (BEC) thermodynamic limit. We consider on certain hyperbolic spaces. In this setting, one obtains a short proof of BEC infinite-volume limit from existence volume-independent spectral gap Laplacian.

We are interested in the development of a numerical method for solving optimal control problems governed by hyperbolic systems of conservation laws. The main difficulty of computing the derivative in the case of shock waves is resolved in the presented scheme. Our approach is based a combination of a relaxation approach in combination with a numerical scheme to resolve the evolution of the tang...

Abstract A class of domain-wall-like solutions of the Skyrme model is obtained analytically. They are described by the tangent hyperbolic function, which is a special limit of the Weierstrass ℘ function. The behavior of one of the two terms in the static energy density is like that of a domain wall. The other term in the static energy density does not vanish but becomes constant at the points f...

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham’s solutions in the Newell’s model. Our ...

In this paper, we show that the analogue of Thurston's asymmetric metric on Teichmüller space flat structures torus is weak Finsler and give a geometric description its unit circle at each point in tangent to space. We then introduce family metrics which interpolate between (which coincides with hyperbolic metric). describe circles family.