Averaging principle for the KdV equation with a small initial value

作者：Yuan, Xiaoping^*; Zhang, Jing^*

来源：Nonlinearity, 2016, 29(2): 603-656.

DOI：10.1088/0951-7715/29/2/603

• periodic perturbed KdV equation
• Hamiltonian PDE
• averaging principle
• unbounded perturbation
• bounded real index-symmetric

The averaging principle with a small initial value is constructed for a Hamiltonian perturbed Korteweg-de Vries (KdV) equation under periodic boundary condition @@@ partial derivative(t)u + u(xxx) +6 u u(x) + (del(u)(K-1(u) + cos(n(0)x) K-2(u)))(x) = 0, x is an element of T := R/(2 pi Z) @@@ where the positive integer n(0) is not divisible by three and K-1 and K-2 are real analytic functions. More precisely, any action I with the small initial value parallel to I(0)parallel to((l) over tildes) <= epsilon evolves slowly over a long time interval: @@@ parallel to I(t) - I(0)parallel to((l) over tildes) less than or similar to epsilon, for any vertical bar t vertical bar less than or similar to epsilon(-5/2), @@@ where s is the index of some space.

• 出版日期2016-2
• 单位复旦大学; 华东师范大学