2013/01/08 by Guan Huang, Huang, Guan
Mathematics · Physics and Astronomy · #34C29 #35Q53 #37K10 #70K65 #74H40 #Advanced Mathematical Physics Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math.DS #msc:34C29 #msc:35Q53 #msc:37K10 #msc:70K65 #msc:74H40
paper · pdf · doi:10.48550/arxiv.1301.1585
25 pages
arxiv created 2013/01/08 · openalex publication_date 2013/01/08 · arxiv updated 2013/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a perturbed KdV equation: [u+uxxx - 6uux = εf(x,u(⋅)), x∈ \mathbbT, ∫_\mathbbT u dx=0.] For any periodic function u(x), let I(u)=(I1(u),I2(u),...)∈ℝ+∞ be the vector, formed by the KdV integrals of motion, calculated for the potential u(x). Assuming that the perturbation εf(x,u(⋅)) is a smoothing mapping (e.g. it is a smooth function εf(x), independent from u), and that solutions of the perturbed equation satisfy some mild a-priori assumptions, we prove that for solutions u(t,x) with typical initial data and for 0\leqslant t\lesssim ε-1, the vector I(u(t)) may be well approximated by a solution of the averaged equation.