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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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