INVARIANT TORI FOR THE HAMILTONIAN DERIVATIVE WAVE EQUATION WITH HIGHER ORDER NONLINEARITY

被引：0
|
作者：
Gao, Meina [1 ]
机构：
[1] Shanghai Polytech Univ, Sch Math Phys & Stat, Shanghai 201209, Peoples R China
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2023年 / 22卷 / 05期
基金：
中国国家自然科学基金;
关键词：
KAM theory; invariant tori; Hamiltonian derivative nonlinear wave equation; QUASI-PERIODIC SOLUTIONS; PARTIAL-DIFFERENTIAL-EQUATIONS; KAM THEOREM; PERTURBATIONS;
D O I：
10.3934/cpaa.2023033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we will study the Hamiltonian derivative wave equation with higher order nonlinearity ytt - yxx + my + (Dy)(5) = 0, x is an element of T :- R/2 pi Z, where m > 0 is a potential and D := root -partial derivative xx + m. We will prove that, for any integer b >= 2, the above equation admits many small amplitude quasi-periodic solutions corresponding to b -dimensional invariant tori of an associated infinite dimensional Hamiltonian system. The proof is based on infinite dimensional KAM theory and partial Birkhoff normal form.
引用
收藏
页码：1429 / 1455
页数：27
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