ALMOST PERIODICITY IN TIME OF SOLUTIONS OF THE KDV EQUATION

被引：19

作者：

Binder, Ilia ^{[1
]}

Damanik, David ^{[2
]}

Goldstein, Michael ^{[1
]}

Lukic, Milivoje ^{[1
,2
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON, Canada

[2] Rice Univ, Dept Math, Houston, TX 77251 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2018年 / 167卷 / 14期

基金：

美国国家科学基金会; 加拿大自然科学与工程研究理事会;

关键词：

KORTEWEG-DEVRIES EQUATION; ABSOLUTELY CONTINUOUS-SPECTRUM; ERGODIC SCHRODINGER-OPERATORS; DE-VRIES EQUATION; NONLINEAR EQUATIONS; INITIAL DATA; POTENTIALS; POINTS;

D O I：

10.1215/00127094-2018-0015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Cauchy problem for the KdV equation partial derivative(t)u - 6u partial derivative(x)u + partial derivative(3)(x)u = 0 with almost periodic initial data u(x,0) = V(x) We consider initial data V, for which the associated Schrodinger operator is absolutely continuous and has a spectrum that is not too thin in a sense we specify, and we show the existence, uniqueness, and almost periodicity in time of solutions. This establishes a conjecture of Deift for this class of initial data. The result is shown to apply to all small analytic quasiperiodic initial data with Diophantine frequency vector.

引用

页码：2633 / 2678

页数：46

共 60 条

[1]

[Anonymous], CAMBRIDGE STUDIES AD

[2] Generic singular spectrum for ergodic Schrodinger operators [J].