Nonlinear Mathematical Physics and Natural Hazards by Boyka Aneva & Mihaela Kouteva-Guentcheva

Author:Boyka Aneva & Mihaela Kouteva-Guentcheva
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.5)

where and are biquadratic polynomials in and given by

The discriminant separability condition

is satisfied with polynomials

Moreover, as it has been explained in [3], all the main steps of the Kowalevski integration procedure from [15] (see also [10]) now follow as easy and transparent logical consequences of the theory of discriminantly separable polynomials.

After we noticed these interesting properties of discriminantly separable polynomials, two natural questions appeared: the question of classification of such polynomials and the question of existence other integrable dynamical systems related to discriminantly separable polynomials. We answered on both questions in our papers: in [4] we presented new examples of dynamical systems obtained by replacing the Kowalevski fundamental equation by some other discriminantly separable polynomail in three variables degree two in each of them and we called such systems systems of Kowalevski type. In [5] we further developed theory of such systems, we obtained procedure for their explicit integration in theta functions of genus two by generalizing integration of Kowalevski top and we also found few examples of well known systems from theory of integrable dynamical systems that could be explicitly integrated by suggested procedure. In [6] we presented classification of discriminantly separable polynomials of three variables degree two in each of them modulo the group of Möbius transformations, as introduced in Corollary 3 of [3]:

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