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Symmetries of systems of the hyperbolic Riccati type. (English. Russian original) Zbl 0990.35011
Theor. Math. Phys. 127, No. 1, 446-459 (2001); translation from Teor. Mat. Fiz. 127, No. 1, 47-62 (2001).
Summary: 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 $$U_{xy} = \left[[U,a],Ux\right]$$ 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.

##### MSC:
 35A30 Geometric theory, characteristics, transformations in context of PDEs 58J70 Invariance and symmetry properties for PDEs on manifolds 35Q55 NLS equations (nonlinear Schrödinger equations)
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