Computability of solutions of the Korteweg-de Vries equation

被引：0
|
作者：
Gay, W
Zhang, BY
Zhong, N
机构：
[1] Univ Cincinnati, Clermont Coll, Batavia, OH 45103 USA
[2] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA
来源：
MATHEMATICAL LOGIC QUARTERLY | 2001年 / 47卷 / 01期
关键词：
initial value problem; KdV equation; Sobolev space;
D O I：
10.1002/1521-3870(200101)47:1<93::AID-MALQ93>3.0.CO;2-C
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study computability of the solutions of the Korteweg-de Vries (KdV) equation u(t) + uu(x) + u(xxx) = 0. This is one of the open problems posted by Pour-El and Richards [25]. Based on Bourgain's new approach to the initial value problem for the KdV equation in the periodic case, we show that the periodic solution u(x, t) of the KdV equation is computable if the initial data is computable.
引用
收藏
页码：93 / 110
页数：18
相关论文
共 50 条
  • [31] Soliton solutions for a variable-coefficient Korteweg-de Vries equation in fluids and plasmas
    Jiang, Yan
    Tian, Bo
    Liu, Wen-Jun
    Sun, Kun
    Qu, Qi-Xing
    PHYSICA SCRIPTA, 2010, 82 (05)
  • [32] Backlund transformation and multi-soliton solutions for the discrete Korteweg-de Vries equation
    Dong, Suyalatu
    Lan, Zhong-Zhou
    Gao, Bo
    Shen, Yujia
    APPLIED MATHEMATICS LETTERS, 2022, 125
  • [33] Separation method for solving the generalized Korteweg-de Vries equation
    Zerarka, A.
    Foester, V.G.
    Communications in Nonlinear Science and Numerical Simulation, 2005, 10 (02) : 217 - 225
  • [34] MODIFIED KORTEWEG-DE VRIES EQUATION AS A SYSTEM WITH BENIGN GHOSTS
    Smilga, Andrei
    ACTA POLYTECHNICA, 2022, 62 (01) : 190 - 196
  • [35] Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain
    Laurent, Camille
    Rosier, Lionel
    Zhang, Bing-Yu
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (04) : 707 - 744
  • [36] On the Form of Dispersive Shock Waves of the Korteweg-de Vries Equation
    Egorova, I.
    Gladka, Z.
    Teschl, G.
    JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, 2016, 12 (01) : 3 - 16
  • [37] WAVE DYNAMICS IN THE EXTENDED FORCED KORTEWEG-DE VRIES EQUATION
    Kapitula, Todd
    De Jong, Nate
    Plaisier, Katelyn
    SIAM JOURNAL ON APPLIED MATHEMATICS, 2011, 71 (03) : 811 - 828
  • [38] BOUNDARY CONTROLLABILITY OF THE KORTEWEG-DE VRIES EQUATION ON A BOUNDED DOMAIN
    Cerpa, Eduardo
    Rivas, Ivonne
    Zhang, Bing-Yu
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (04) : 2976 - 3010
  • [39] Homotopy Analysis of Korteweg-de Vries Equation with Time Delay
    Raees, A.
    Xu, H.
    SIXTH INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS (ICNM-VI), 2013, : 229 - 233
  • [40] Existence for Korteweg-de Vries-type equation with delay
    Zhihong Zhao
    Erhua Rong
    Xiangkui Zhao
    Advances in Difference Equations, 2012
12345