Solitons and instantons in vacuum stability

We investigate the instanton solutions and soliton-like bubbles in vacuum dynamics. We show that the results of recent CERN experiments lead to the fact that our vacuum is safe. We present a new mechanism, where the space-time dimension plays an important role, that explains why our Universe is stable. We provide new evidence that supports a process for the origin of Matter-Antimatter Asymmetry recently introduced by other scientists. We examine confinement in the context of escape problems. We discuss multiverse, string theory landscape, and extra-dimensions using our framework. We use our solutions to introduce some hypotheses about Dark Matter and Dark Energy

An escape of vector matter-wave soliton from a parabolic trap

We show that a vector matter–wave soliton in a Bose–Einstein condensate (BEC) loaded into an optical lattice can escape from a trap formed by a parabolic potential, resembling a Hawking emission. The particle–antiparticle pair is emulated by a low-amplitude bright–bright soliton in a two-component BEC with effective masses of opposite signs. It is shown that the parabolic potential leads to a spatial separation of BEC components. One component with chemical potential in a semi-infinite gap exerts periodical oscillations, while the other BEC component, with negative effective mass, escapes from the trap. The mechanism of atom transfer from one BEC component to another by spatially periodic linear coupling term is also discussed.Y.V.B. acknowledges the support from Portuguese Foundation for Science and Technology (FCT) through Grant No. UID/FIS/04650/2013. M.A.G.-N. thanks for the financial support of FONDECYT project 11130450.info:eu-repo/semantics/publishedVersio

Hawking-like emission in kink-soliton escape from a potential well.

The escape of solitons over a potential barrier is analysed within the framework of a nonlinear Klein–Gordon equation. It is shown that the creation of a kink–antikink pair near the barrier through an internal mode instability can be followed by escape of the kink in a process analogous to Hawking radiation. These results have important implications in a wider context, including stochastic resonance and ratchet systems, which are also discussed

Rogue waves and solitons on a cnoidal background

Solutions of the nonlinear Schr¨odinger equation, appearing as rogue waves on a spatially-periodic background envelope, are obtained using the Darboux transformation scheme. Several particular examples are illustrated numerically. These include soliton and breather solutions on a periodic background as well as higher-order structures. The results enrich our knowledge of possible analytic solutions that describe the appearance of rogue waves in a variety of situations.The authors acknowledge the support of the Australian Research Council (Discovery Project number DP110102068). N.A. and A.A. acknowledge support from the Volkswagen Stiftung