J. Cuevas

Topical 5-aminolevulinic acid photodynamic therapy for the treatment of unilesional mycosis fungoides: a report of two cases and review of the literature

Background  Unilesional mycosis fungoides (MF) is a rare variant of cutaneous T‐cell lymphoma (CTCL), characterized clinically by a solitary lesion and by histopathological features indistinguishable from multilesional MF. The photodynamic therapy (PDT) is a new and effective treatment of precancerous lesions and non‐melanoma skin cancers. In recent years it has been used successfully for the treatment of MF.

Solitons for the cubic–quintic nonlinear Schrödinger equation with time- and space-modulated coefficients

In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic–quintic nonlinear Schrodinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose–Einstein condensates and nonlinear optics.

Moving breathers in a DNA model with competing short- and long-range dispersive interactions

Abstract Moving breathers is a means of transmitting information in DNA. We study the existence and properties of moving breathers in a DNA model with short-range interaction, due to the stacking of the base pairs, and long-range interaction, due to the finite dipole moment of the bond within each base pair. In our study, we have found that mobile breathers exist for a wide range of the parameter values, and the mobility of these breathers is hindered by the long-range interaction. This fact is manifested by: (a) an increase of the effective mass of the breather with the dipole–dipole coupling parameter; (b) a poor quality of the movement when the dipole–dipole interaction increases; (c) the existence of a threshold value of the dipole–dipole coupling above which the breather is not movable. An analytical formula for the boundaries of the regions where breathers are movable is calculated. Concretely, for each value of the breather frequency, one can obtain the maximum value of the dipole–dipole coupling parameter and the maximum and minimum values of the stacking coupling parameter where breathers are movable. Numerical simulations show that, although the necessary conditions for the mobility are fulfilled, breathers are not always movable. Finally, the value of the dipole–dipole coupling constant is obtained through quantum chemical calculations. They show that the value of the coupling constant is small enough to allow a good mobility of breathers.

Breathers in oscillator chains with Hertzian interactions

We prove nonexistence of breathers (spatially localized and time-periodic oscilla- tions) for a class of Fermi-Pasta-Ulam lattices representing an uncompressed chain of beads interacting via Hertzs contact forces. We then consider the setting in which an additional on-site potential is present, motivated by the Newtons cradle under the effect of gravity. Using both direct numerical computations and a simplified asymptotic model of the oscillator chain, the so-called discrete p-Schrodinger (DpS) equation, we show the existence of discrete breathers and study their spectral prop- erties and mobility. Due to the fully nonlinear character of Hertzian interactions, breathers are found to be much more localized than in classical nonlinear lattices and their motion occurs with less dispersion. In addition, we study numerically the excitation of a traveling breather after an impact at one end of a semi-infinite chain. This case is well described by the DpS equation when local oscillations are faster than binary collisions, a situation occuring e.g. in chains of stiff cantilevers decorated by spherical beads. When a hard anharmonic part is added to the local potential, a new type of traveling breather emerges, showing spontaneous direction-reversing in a spatially homogeneous system. Finally, the interaction of a moving breather with a point defect is also considered in the cradle system. Almost total breather reflec- tions are observed at sufficiently high defect sizes, suggesting potential applications of such systems as shock wave reflectors.

Moving discrete breathers in a Klein?Gordon chain with an impurity

We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein?Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.

Discrete breathers in a forced-damped array of coupled pendula: modeling, computation, and experiment.

In this work, we present a mechanical example of an experimental realization of a stability reversal between on-site and intersite centered localized modes. A corresponding realization of a vanishing of the Peierls-Nabarro barrier allows for an experimentally observed enhanced mobility of the localized modes near the reversal point. These features are supported by detailed numerical computations of the stability and mobility of the discrete breathers in this system of forced and damped coupled pendula. Furthermore, additional exotic features of the relevant model, such as dark breathers are briefly discussed.

Solitons in quasi-one-dimensional Bose-Einstein condensates with competing dipolar and local interactions

We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for subfundamental solitons is found in the second finite band gap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the opposite case of the DD repulsion, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, they merge or pass through each other at small and large velocities, respectively. In the presence of the local repulsion, slowly moving solitons bounce from each other.

Demonstration of the stability or instability of multibreathers at low coupling

Abstract Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrodinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.

Influence of moving breathers on vacancies migration

A vacancy defect is described by a Frenkel–Kontorova model with a discommensuration. This vacancy can migrate when interacts with a moving breather. We establish that the width of the interaction potential must be larger than a threshold value in order that the vacancy can move forward. This value is related to the existence of a breather centred at the particles adjacent to the vacancy.

Beating dark–dark solitons in Bose–Einstein condensates

Motivated by recent experimental results, we study beating dark?dark (DD) solitons as a prototypical coherent structure that emerges in two-component Bose?Einstein condensates. We showcase their connection to dark?bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark?anti-dark soliton states. Finally, we consider the dynamics and interactions of two beating DD solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction.