Geodesic
Symmetries of Systems of the Hyperbolic Riccati Type
Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 47-62

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Let $\mathfrak G=\bigoplus_{i\in\mathbb Z}\mathfrak G_i$ be a Kac–Moody algebra, $U(x,y)$ be a function defined in $\mathfrak G_{-1}$, and $a$ be a constant element of $\mathfrak G_1$. We prove that the equation $U_{xy}=\bigl[[U,a],U_x\bigr]$ has two symmetry hierarchies connected by a gauge transformation. In particular, the well-known Konno equation appears in the case of the algebra $A_1^{(1)}$. The corresponding symmetry hierarchies contain the nonlinear Schrödinger and the Heisenberg magnet equations. 
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     author = {A. A. Bormisov and F. Kh. Mukminov},
     title = {Symmetries of {Systems} of the {Hyperbolic} {Riccati} {Type}},
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A. A. Bormisov; F. Kh. Mukminov. Symmetries of Systems of the Hyperbolic Riccati Type. Teoretičeskaâ i matematičeskaâ fizika, Tome 127 (2001) no. 1, pp. 47-62. http://geodesic.mathdoc.fr/item/TMF_2001_127_1_a3/