Geodesic
First-Order Differential Substitutions for Equations Integrable on~$\mathbb S^n$
Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 178-189.

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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.
Keywords: vector evolution equation, differential substitution, Bäcklund transformation, pseudosymmetry, Schwartz–KdV equation.
Mots-clés : Miura-type transformation 
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M. Yu. Balakhnev. First-Order Differential Substitutions for Equations Integrable on~$\mathbb S^n$. Matematičeskie zametki, Tome 89 (2011) no. 2, pp. 178-189. http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a1/

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