A Generic Nonlinear Evolution Equation of Magnetic Type II. Particular Solutions

We consider a matrix nonlinear partial differential equation that generalizes Heisenberg ferromagnet equation. This generalized Heisenberg ferromagnet equation is completely integrable with a linear bundle Lax pair related to the pseudo-unitary algebra. This allows us to explicitly derive particular solutions by using dressing technique. We shall discuss two classes of solutions over constant background: soliton-like solutions and quasi-rational solutions. Both classes have their analogues in the case of the Heisenberg ferromagnet equation related to the same Lie algebra.Comment: 19 page

Nonlocal Reductions of a Generalized Heisenberg Ferromagnet Equation

We study nonlocal reductions of coupled equations in $1+1$ dimensions of the Heisenberg ferromagnet type. The equations under consideration are completely integrable and have a Lax pair related to a linear bundle in pole gauge. We describe the integrable hierarchy of nonlinear equations related to our system in terms of generating operators. We present some special solutions associated with four distinct discrete eigenvalues of scattering operator. Using the Lax pair diagonalization method, we derive recurrence formulas for the conserved densities and find the first two simplest conserved densities.Comment: 14 pages. arXiv admin note: substantial text overlap with arXiv:1711.0635

Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models

We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces and their reductions. We briefly outline the direct and the inverse scattering method for the relevant Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing method to obtain the two-soliton solution and analyze the soliton interactions of the MNLS equations and some of their reductions.Comment: SPIE UNO-09-UN101-19, SPIE Volume: 7501, (2009

Relation between first lactation milk yield and functional traits in dairy cows

The aim of the study was to analyze the relationship between first lactation milk yield (FLMY) and age at first calving (AFC), longevity and productive life in dairy cows. The study covered 944 Holstein cows housed in 5 dairy cattle farms in Bulgaria. All cows from the five farms culled in the period 2012–2018 with FLMY data were included. The average AFC for all culled cows included in the study was relatively high for the Holstein-Friesian breed - 29.75 months. The average FLMY of the herds included in the study was 7,660.94 kg with significant herd variation from 5,899.09 kg to 8,646.0 kg. Significant effect of the herd (P < 0.001), AFC and the associated effect of the herd and AFC (P < 0.05) on the average FLMY were found. The highest FLMY was reported in primiparous with AFC of 28–30 months – 7,860.8 kg, and the lowest in those with AFC ≤ 24 months – 7322.8 kg. In the herd with the lowest average FLMY - 5,899.09 kg 27.5% of the heifers had calved at age over 34 months. A statistically significant effect of AFC (P < 0.001) was found on longevity, whereas the productive life was significantly influenced by FLMY (P < 0.05). A tendency for higher longevity for cows with higher AFC of 34–37 months and over 37 months – 5.9 and 5.8 years, respectively was observed. The lowest were the longevity values for cows calved at age up to 24 months – 4.9 years. The cows with the lowest average FLMY (up to 4,000 kg) had the shortest productive. Both very low and high AFC were associated with lower first lactation cow productivity and shorter productive life. The losses for farmers were greater when keeping a high AFC in heifers, which increases the cost for housing them, and the lower productivity and longer productive life reduce the probability

Rational Bundles and Recursion Operators for Integrable Equations on A.III-type Symmetric Spaces

We analyze and compare the methods of construction of the recursion operators for a special class of integrable nonlinear differential equations related to A.III-type symmetric spaces in Cartan's classification and having additional reductions.Comment: 13 pages, 1 figur

Reductions of integrable equations on A.III-type symmetric spaces

We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to this symmetric space as an element of the reduction group and restrict generic Lax operators to this symmetric space. The symmetries of the Lax operator are inherited by the fundamental analytic solutions and give a characterization of the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl