Premium
Computability of Solutions of the Korteweg‐de Vries Equation
Author(s) -
Gay William,
Zhang BingYu,
Zhong Ning
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200101)47:1<93::aid-malq93>3.0.co;2-c
Subject(s) - korteweg–de vries equation , mathematics , computability , initial value problem , value (mathematics) , pure mathematics , mathematical analysis , discrete mathematics , nonlinear system , physics , statistics , quantum mechanics
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.