4 papers
From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture
Renato Calleja, Carlos GarcÃa-Azpeitia, Olivier Hénot +2
For the three body problem with equal masses, we prove that the most symmetric continuation class of Lagrange's equilateral triangle solution, also referred to as the fami…
Computer-Assisted Proofs of Gap Solitons in Bose-Einstein Condensates
Miguel Ayala, Carlos GarcÃa-Azpeitia, Jean-Philippe Lessard
We provide a framework for turning a numerical simulation of a gap soliton in the one-dimensional Gross-Pitaevskii equation into a rigorous mathematical proof of its existence. The…
Symmetric periodic solutions in the generalized Sitnikov Problem with homotopy methods
Carlos Barrera-Anzaldo, Carlos GarcÃa-Azpeitia
The paper investigates a generalization of the classical Sitnikov problem, concentrating on the movement of a satellite along the Z-axis as it interacts with primary bodies in…
Global Bifurcation In Four-Component Bose-Einstein Condensates In Space
Carlos GarcÃa-Azpeitia, Anna GoÅÈ©biewska, Wieslaw Krawcewicz +1
We analyze a system of coupled Bose-Einstein condensates in the domain of a unitary ball in . The coupling is due to atom-to-atom interactions that occur between diff…