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math.DS2025
Spatially inhomogeneous two-cycles in an integrodifference equation
Kevin Church, Kevin Constantineau, Jean-Philippe Lessard
In this work, we prove the existence of a 2-cycle in an integrodifference equation with a Laplace kernel and logistic growth function, connecting two non-trivial fixed points of th…
math.DS2025
Computer-Assisted Proofs of Gap Solitons in Bose-Einstein Condensates
Miguel Ayala, Carlos García-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…