Elsevier

Applied Mathematics Letters

Volume 79, May 2018, Pages 211-219
Applied Mathematics Letters

Integrability aspects of some two-component KdV systems

https://doi.org/10.1016/j.aml.2017.12.018Get rights and content
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Abstract

Some two-component Korteweg–de Vries systems are studied by prolongation technique and Painlevé analysis. Especially, the two-component KdV system conjectured to be integrable by Foursov is proved to be both Lax integrable and P-integrable. Its conservation laws are investigated based on the obtained Lax pair. Furthermore, it is shown that the three two-component Korteweg–de Vries systems are identical under certain invertible linear transformations. Finally, the auto-Bäcklund transformation and some exact solutions for the two-component Korteweg–de Vries system are derived explicitly.

Keywords

Prolongation structure
Lax pair
Conservation law
Painlevé test
Auto-Bäcklund transformation

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