Mathematical Notes

, Volume 89, Issue 1–2, pp 184–193 | Cite as

First-order differential substitutions for equations integrable on \( \mathbb{S}^n \)

  • M. Yu. BalakhnevEmail author


We determine necessary conditions under which integrable vector evolution equations of third order admit Miura-type transformations. For equations integrable on the n-dimensional sphere, we obtain first-order differential substitutions.


vector evolution equation Miura-type transformation differential substitution Bäcklund transformation pseudosymmetry Schwartz-KdV equation 


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© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Orlov State Technical UniversityOrlovRussia

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