2015/06/04 by Paulo E G Assis, P. E. G. Assis
Mathematics · Physics and Astronomy · #Field (mathematics) #Geometry #Integrable system #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Scattering #Symmetry (geometry) #Theoretical physics #hep-th #math-ph #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.1088/1751-8113/49/24/245201
arxiv created 2015/06/04 · openalex publication_date 2016/05/09 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Observations of almost stable scattering in nonintegrable models have been reinforced and a framework is proposed to describe quasi-integrability in terms of symmetry. This new mechanism can be used to regard symmetry in classical field theories as a guiding principle to also select relevant systems when it comes to integrability properties. It turns out that the if a deformed Lax pair is invariant under this symmetry, corresponding to the unbroken -symmetric regime, quasi-integrable excitations are produced with asymptotically conserved charges. A generic nonlinear field equation is used in order to verify the validity of the assumptions but results for a specific non-integrable class of models are also presented. A set of quasi-integrable excitations is investigated and shown to have spectral functions with appropriate properties, which might lead to the determination of the almost conserved charges.