Browsing by Author "Yanovski A.B."

Now showing 1 - 3 of 3
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    Hermitian and pseudo-hermitian reduction of the GMV auxiliary system. Spectral properties of the recursion operators
    (2019-01-01) Yanovski A.B.; Valchev T.I.
    We consider simultaneously two different reductions of a Zakharov-Shabat’s spectral problem in pole gauge. Using the concept of gauge equivalence, we construct expansions over the eigenfunctions of the Recursion Operators related to the afore-mentioned spectral problem with arbitrary constant asymptotic values of the potential functions. In doing this, we take into account the discrete spectrum of the scattering operator. Having in mind the applications to the theory of the soliton equations associated to the GMV systems, we show how these expansions modify depending on the symmetries of the functions we expand.
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    Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. I. Auxiliary System and Fundamental Properties
    (2018-04-03) Yanovski A.B.; Valchev T.I.
    We consider an auxiliary spectral problem originally introduced by Gerdjikov, Mikhailov and Valchev (GMV system) and its modification called pseudo-Hermitian reduction which is extensively studied here for the first time. We describe the integrable hierarchies of both systems in a parallel way and construct recursion operators. Using the concept of gauge equivalence, we construct expansions over the eigenfunctions of recursion operators. This permits us to obtain the expansions for both GMV systems with arbitrary constant asymptotic values of the potential functions in the auxiliary linear problems.
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    Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. II. Special Solutions
    (2018-07-03) Valchev T.I.; Yanovski A.B.
    This paper is a continuation of our previous work in which we studied a sl (3, ℂ) Zakharov-Shabat type auxiliary linear problem with reductions of Mikhailov type and the corresponding integrable hierarchy of nonlinear evolution equations. Now, we shall demonstrate how one can construct special solutions over constant back- ground through Zakharov-Shabat’s dressing technique. That approach will be illustrated on the example of the generalized Heisenberg ferromagnet equation related to the linear problem for sl (3, ℂ). In doing this, we shall discuss the differences between the Hermitian and pseudo-Hermitian cases.