Classification of Integrable Divergent N-Component Evolution Systems

On a classification of integrable vectorial evolutionary equations

“…The auto-Bäcklund transformations (4.9), (4.10), (4.18) and (4.19) have been found in [7]. The auto-Bäcklund transformations for equations (3.3)-(3.7) have been found in [6].…”

“…Remark 1. Equations (3.1) and (3.2) differ from (1.1) by a dilatation of u; equations (3.3) -(3.7) have been presented in [6]. Equations (3.14) and (3.15) have been presented in [7] in a different form.…”

“…A complete classification of the isotropic integrable equations (1.6) on a sphere has been obtained in [5]. A complete classification of the integrable divergent equations (1.6) has been presented in [6]. A complete list of the isotropic integrable equations (1.6) with f 2 = 0 has been presented in [7].…”

Superposition formulas for integrable vector evolutionary equations on a Sphere

“…There are some other articles devoted to the vector equation in R n having the form of conservation laws were presented in [2], and a special case was considered in [3]. Integrable anisotropic evolutionary equations on the n-dimensional sphere were classified in [4].…”

“…Integrable anisotropic evolutionary equations on the n-dimensional sphere were classified in [4]. However, superposition formulas were found only for a few equations, namely for the vector Schwarz-KdV [2], two generalizations of the mKdV [5], and the Landau-Lifshitz generalization [6].…”