2025/10/06 by Boyang Wu, Wu, Boyang, Miguel Onorato +5 · 1 citation
Computer Science · Earth and Planetary Sciences · Materials Science · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Numerical Analysis (math.NA) #Ocean Waves and Remote Sensing #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.2510.04831
openalex publication_date 2025/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we provide a validity condition for the normal form transformation to remove the non-resonant cubic terms in the β-FPUT system. We show that for a wave field with random phases, the normal form transformation is valid by dominant probability if β≪ 1/N1+ε, with N the number of masses and ε an arbitrarily small constant. To obtain this condition, a bound is needed for a summation in the transformation equation, which we prove rigorously in the paper. The condition also suggests that the importance of the non-resonant terms in the evolution equation is governed by the parameter βN. We design numerical experiments to demonstrate that this is indeed the case for spectra at both thermal-equilibrium and out-of-equilibrium conditions. The methodology developed in this paper is applicable to other Hamiltonian systems where a normal form transformation needs to be applied.