On kinks and other travelling-wave solutions of a modified sine-Gordon equation

We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of superconductors and other remarkable physical phenomena. The perturbation of the equation consists of a constant forcing term and a linear dissipative term. On the real line candidate orbitally stable solutions with bounded energy density are either the constant one, or of kink (i.e. soliton) type, or of array-of-kinks type, or of "half-array-of-kinks" type. While the first three have unperturbed analogs, the last type is essentially new. We also propose a convergent method of successive approximations of the (anti)kink solution based on a careful application of the fixed point theorem.Comment: Latex file, 25 pages, 4 figures. Final version to appear in "Meccanica

On Geometrical and Physical consequences of using certain special classes of comoving physical frames of reference.

In the case of spherical symmetry, we deal with motions comoving with some classes of reference frames associated to isotropic coordinates

On geometrical and physical consequencesof using certain special classes of comoving physical frames ofreference

This paper develops the study of the geometrical characteristics of the class of frames of reference associated with the two well known sets of coordinates: Levi-Civita's curvature coordinates and gaussian polar coordinates. In particular, through the separate invariant formulation of the initial data problem and of the restricted evolution problem, the analysis is applied to a spherically symmetric perfect uid, whose stream lines coincide with those of the above mentioned class of frames

Existence and uniqueness results for a class of non linear models

The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are determined and are applied to an equivalent integro differential formulation of the problem. By the fixed point theorem, existence and uniqueness results are obtained

Fenomeni di propagazione e diffusione in superconduttivita'

La dinamica delle giunzioni di Josephson della superconduttivita' e' descritta dall' equazione di sine - Gordon perturbata (PSGE), che risulta un classico esempio di equazione iperbolica non lineare perturbata da termini lineari del terzo ordine caratterizzati da un piccolo parametro epsilon. Si studia il problema di valori iniziali per tale equazione e si analizza la questione di piccolo parametro che si ha quando epsilontende a 0. Infine si determinano gli intervalli di tempo in cui la propagazione ondosa prevale sugli effetti diffusivi e l'ordine di grandezza di tali effetti