| Title: |
Computer-Assisted Proofs of Gap Solitons in Bose-Einstein Condensates |
| Authors: |
Ayala, Miguel; García-Azpeitia, Carlos; Lessard, Jean-Philippe |
| Publication Year: |
2025 |
| Subject Terms: |
Dynamical Systems; Analysis of PDEs |
| Description: |
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. These nonlinear localized solutions play a central role in the study of Bose-Einstein condensates (BECs). We reformulate the problem of proving their existence as the search for homoclinic orbits in a dynamical system. We then apply computer-assisted proof techniques to obtain verifiable conditions under which a numerically approximated trajectory corresponds to a true homoclinic orbit. This work also presents the first examples of computer-assisted proofs of gap solitons in the Gross-Pitaevskii equation on non-perturbative parameter regimes. |
| Document Type: |
Working Paper |
| DOI: |
10.1007/s00332-026-10242-2 |
| Access URL: |
http://arxiv.org/abs/2503.04701 |
| Accession Number: |
edsarx.2503.04701 |
| Database: |
arXiv |