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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.

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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