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 
@article{MZM_2011_89_2_a1,
     author = {M. Yu. Balakhnev},
     title = {First-Order {Differential} {Substitutions} for {Equations} {Integrable} on~$\mathbb S^n$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {178--189},
     publisher = {mathdoc},
     volume = {89},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_2_a1/}
}
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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/