This article is cited in 2 papers

First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$

M. Yu. Balakhnev

Orel State Technical University

Abstract: 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, Miura-type transformation, differential substitution, Bäcklund transformation, pseudosymmetry, Schwartz–KdV equation.

UDC: 517.957

Received: 13.01.2009
Revised: 22.06.2010

DOI: 10.4213/mzm6644

 English version: Mathematical Notes, 2011, 89:2, 184–193

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