Some methods for generating solutions to the Korteweg–de Vries equation

The constraint equation which must hold for the reciprocal of a known solution for the Korteweg–de Vries (KdV) equation to be a solution itself is derived. These reciprocal solutions are required to satisfy a differential equation which is in fact a Painlevé equation. A differential constraint is also derived which allows the product of two solutions of the KdV equation to be a new solution as well.

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Year of publication:	2004
Authors:	Bracken, Paul
Published in:	Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 335.2004, 1, p. 70-78
Publisher:	Elsevier
Subject:	KdV equation \| Differential constraints \| Soliton \| Painlevé equation

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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