Quasi-periodic solutions for 1D wave equation with higher order nonlinearity期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Quasi-periodic solutions for 1D wave equation with higher order nonlinearity

Authors:	Meina Gao Jianjun Liu

Affiliation:	1. School of Science, Shanghai Second Polytechnic University, Shanghai 201209, PR China;2. School of Mathematical Science, Fudan University, Shanghai 200433, PR China

Abstract:	In this paper, one-dimensional (1D) nonlinear wave equation $u_{t t} ? u_{x x} + m u + u^{5} = 0$ on the finite x-interval $[0, π]$ with Dirichlet boundary conditions is considered. It is proved that there are many 2-dimensional elliptic invariant tori, and thus quasi-periodic solutions for the above equation. The proof is based on infinite-dimensional KAM theory and partial Birkhoff normal form.

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