2023/06/26 by Trevor A. Norton, C. Eugene Wayne, Norton, Trevor +1
Mathematics · Physics and Astronomy · #35Q53 #Advanced Mathematical Physics Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Primary 37K60 #Secondary 37K40
paper · pdf · doi:10.48550/arxiv.2306.14999
openalex publication_date 2023/06/26 · openalex created_date 2023/06/29 · openalex updated_date 2026/07/28
It is well known that the Korteweg-de Vries (KdV) equation and its generalizations serve as modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation estimates and other such results have been proved in this case. However, situations in which the defocusing modified KdV (mKdV) equation is expected to be the modulation equation have been much less studied. As seen in numerical experiments, the kink solution of the mKdV seems essential in understanding the β-FPUT recurrence. In this paper, we derive explicit approximation results for solutions of the FPUT using the mKdV as a modulation equation. In contrast to previous work, our estimates allow for solutions to be non-localized as to allow approximate kink solutions. These results allow us to conclude meta-stability results of kink-like solutions of the FPUT.