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Computability of Solutions of the Korteweg-de Vries Equation

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Mathematical Logic Quarterly 47 (1):93-110 (2001)
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Abstract

In this paper we study computability of the solutions of the Korteweg‐de Vries (KdV) equation ut + uux + uxxx = 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.

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10.1002/1521-3870(200101)47:1<93::aid-malq93>3.0.co;2-c

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Nian Zhong
Wuhan University

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