REAL-VALUED NON-ANALYTIC SOLUTIONS FOR THE GENERALIZED KORTEWEG-DE VRIES EQUATION

被引：4

作者：

Himonas, A. Alexandrou ^{[1
]}

Petronilho, Gerson ^{[2
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 08期

基金：

巴西圣保罗研究基金会;

关键词：

Generalized Korteweg-de Vries equation; gKdV; Cauchy problem; periodic; non-periodic; analytic solutions; NONLINEAR SCHRODINGER-EQUATIONS; GLOBAL WELL-POSEDNESS; DEVRIES EQUATION; KDV EQUATION; ILL-POSEDNESS; ANALYTICITY; UNIQUENESS;

D O I：

10.1090/S0002-9939-2011-10983-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In both the periodic and non-periodic cases, non-analytic in time solutions to the Cauchy problem of the gKdV equation are constructed with real-valued analytic initial data when k is not a multiple of four. In the case that k = 4l, that is, the non-linearity is of the form u(4l)partial derivative(x)u, where l is a positive integer, then non-analytic in time solutions are available only for complex-valued initial data.

引用

页码：2759 / 2766

页数：8

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