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On the Bäcklund transformation and Hamiltonian properties of superevaluation equations. (English) Zbl 0614.70014

This paper investigates the evolution equations connected with the spectral problem \(\psi_ x=U\psi\) where U is a \(3\times 3\) matrix containing both commuting and anticommuting potentials. The authors derive first the corresponding hierarchy of evolution equations, and then obtain the Bäcklund transformation in the special case when two of the potentials are set to be constant. To establish the Hamiltonian structure the authors extend the method of M. Boiti, F. Pempinelli and G. Z. Tu [Nuovo Cimento, B 79, 231-265 (1984)] to the case of supervaluation equations and thereby obtain the recursion operators which generates in its turn an infinite number of symmetries of the equations in the hierarchy.
Regretfully this paper contains a number of errors. For example, the commutation rules for generators, the expression for the operator £.
Reviewer: Tu Guizhang

MSC:

70H05 Hamilton’s equations
35Q99 Partial differential equations of mathematical physics and other areas of application
17B99 Lie algebras and Lie superalgebras
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