3 papers
math.DS2026
Lagrange Stability for Reversible Duffing Equations with Quasi-Periodic Coefficients
Huining Xue
We consider \[ \ddot x+f(x,ωt)\dot x+g(x,ωt)=0, \] where \[ f(x,θ)=\sum_{j=0}^{m}a_j(θ)x^{2j+1},\qquad g(x,θ)=x^{2n+1}+\sum_{j=0}^{n-1}b_j(θ)x^{2j+1}. \] The coefficient functions…
math.DS2025
Construction of periodic solutions of multi-dimensional nonlinear wave equations with unbounded perturbation
Huining Xue, Zuhong You, Xiaoping Yuan
By applying the Craig-Wayne-Bourgain (CWB) method, we establish the persistence of periodic solutions to multi-dimensional nonlinear wave equations (NLW) with unbounded perturbatio…
math.DS2024
Long time stability for KAM tori of the derivative nonlinear Schrödinger equation
Shengqing Hu, Huining Xue, Xiaoping Yuan
This paper is concerned with the long time stability of KAM tori for a class of derivative nonlinear Schrödinger equations subjected to periodic boundary condition.