A Jacobian generalization of the pseudo-Nambu–Goldstone boson potential

We enlarge the classes of inflaton and quintessence fields by generalizing the pseudo-Nambu–Goldstone boson potential by means of elliptic Jacobian functions, which are characterized by a parameter [Formula: see text]. We use such a generalization to implement an inflationary era and a late acceleration of the universe. As an inflationary model, the Jacobian generalization leads us to a number of e-foldings and a primordial spectrum of perturbations compatible with the Planck Collaboration 2015. As a quintessence model, a study of the evolution of its equation-of-state (EoS) and its [Formula: see text]–[Formula: see text] plane helps us to classify it as a thawing model. This allows us to consider analytical approximations for the EoS recently discovered for thawing quintessence. By using JLA supernovae Ia and Hubble parameter [Formula: see text] data sets, we perform an observational analysis of the viability of the model as quintessence.

Exact Localized and Periodic Solutions of the Ablowitz-Ladik Discrete Nonlinear Schrödinger System

We have studied, analytically, the Ablowitz-Ladik discrete nonlinear Schr¨odinger system. We have found a set of exact solutions which includes as particular cases periodic solutions in terms of elliptic Jacobian functions, bright and dark soliton solutions, and quasi-periodic solutions. We have also found the range of parameters where each exact solution exists. - PACS: 02.30.Jr, 05.45.Yv, 42.65.Tg, 02.30.Gp.