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We find all non-abelian generalizations of $\text{P}_1 - \text{P}_6$ Painlevé systems such that the corresponding autonomous system obtained by freezing the independent variable is integrable. All these systems have isomonodromic Lax representations.

The highest critical mass of neutron stars (NSs) was reviewed in the context of equation of state and observationsl results/ It was predicted that the maximum NS mass (MNS) exists in the range MNS ~ 2.2-2.9 M_Sun. However, recent observations of gravitationsl waves and other studies had suggested the higher mass limit of NSs, MNS ~ 3/2 M_Sun. The NS mass up to the value of MNS ~ 2 M_Sun is well understood, and with such a mass value it was meaning ful to discuss the "mass gap" ("m-gap") between the NS and black hole (BH) collapsars.The "m-gap" exists in between the highest mass of NS and the lowest mass of BH collapsars (Mm-gap ~ 2-5 M_Sun). in the mass distribution, the maximim population of NSs and BHs is located at MNS = 1.4 M_Sun and MBH = 6.7 M_Sun, respectively. However, recent ofservational results predicted filling the "m-gap" by the compact objects. In this paper, the concept of gravidynamics was reported to resolve the problem of peak likelihood value of gravitational mass at Mpeak = 6.7 M_Sun and the "m-gap" (Mm-gap ~ 2-5 M_Sun). This concept was based on a non-metric scalar-tensor model of gravitational interaction with localizable field energy. The gravidynamics model shows the total mass (MQ) of a compact relativistic object filled with matter of quark-gluon plasma of the radius r* = GMQ/c2 ~ 10 km, consistent with the "m-gap". It was conceptualized that the total measurable gravitational mass of such an extremely dense object consists of both matter and field, which is described by scalar-tensor components. This model is also useful for predicting the collapsars within the "m-gap"., 25 pages, 4 figures, accepted for publication in Astrophysical Bulletin, vol.77. arXiv admin note: text overlap with arXiv:1309.6635, arXiv:1006.2834, arXiv:1909.05804 by other authors

We study non-abelian systems of Painlevé type. To derive them, we introduce an auxiliary autonomous system with the frozen independent variable and postulate its integrability in the sense of the existence of a non-abelian first integral that generalizes the Okamoto Hamiltonian. All non-abelian P6-P2-systems with such integrals are found. A coalescence limiting scheme is constructed for these non-abelian Painlevé systems. This allows us to construct an isomonodromic Lax pair for each of them.

All Hamiltonian non-abelian Painlevé systems of ${\rm{P}}_{1}-{\rm{P}}_{6}$ type with constant coefficients are found. For ${\rm{P}}_{1}-{\rm{P}}_{5}$ systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new ${\rm{P}}_{3}^{\prime}$ and ${\rm{P}}_{5}$ systems thus obtained, we find isomonodromic Lax pairs for them.

For all non-equivalent matrix systems of Painlevé-4 type found by authors in arXiv:2107.11680, isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlevé-2 equations are found.

Using the Painlevé--Kovalevskaya test, we find several new matrix generalizations of the Painlevé-4 equation. Some limiting transitions reduce them to known matrix Painlevé-2 equations.

Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair consisting of a triple Jordan system and a skew-symmetric bilinear operation. If this operation is a Lie bracket, then we arrive at the Lie-Jordan algebras, 22 pages. arXiv admin note: substantial text overlap with arXiv:1804.06396

The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand side are considered. Such systems are associated with associative algebras and, more generally, with non-associative algebraic structures, whose structural constants are defined by the coefficients of the system under consideration. We explore which structures correspond to polynomial integrable models. Integrable systems polynomial in derivatives are described in geometric terms. The third part we consider integrable vector izotropic and anizotropic systems., 149 pages

We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with an associative version of Young-Baxter equations, we study a bi-hamiltonian property of the linear-quadratic pencil of the double Poisson structure and propose a classification of the quadratic double Poisson brackets in the case of the algebra with two free generators. Many new examples of quadratic double Poisson brackets are proposed., Comment: 19 pages, latex

FeXMn1-XS (0, Comment: 5 pages, 7 figures,references,text;the final variant will submitted in Phys.Rev.B

We consider a special class of linear and quadratic Poisson brackets related to ODE systems with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets and found the corresponding hierarchy of integrable models, which generalizes the two-component Manakov's matrix system in the case of arbitrary number of matrices., Comment: 9 pages, latex

We present BV RI photometric and low-resolution spectroscopic investigation of a type II core-collapse supernova (SN) 2008gz, which occurred in a star forming arm and within a half-light radius (solar metallicity region) of a nearby spiral galaxy NGC 3672. The SN event was detected late and a detailed investigation of its light curves and spectra spanning 200 days suggest that it is an event of type IIP similar to archetypal SNe 2004et and 1999em. However, in contrast to other events of its class, the SN 2008gz exhibits rarely observed V magnitude drop of 1.5 over the period of a month during plateau to nebular phase. Using 0.21 mag of Av as a lower limit and a distance of 25.5 Mpc, we estimate synthesized $^{56}$Ni mass of 0.05 \pm 0.01 M* and a mid-plateau Mv of -16.6 \pm 0.2 mag. The photospheric velocity is observed to be higher than that was observed for SN 2004et at similar epochs, indicating explosion energy was comparable to or higher than SN 2004et. Similar trend was also seen for the expansion velocity of H-envelopes. By comparing its properties with other well studied events as well as by using a recent simulation of pre-SN models of Dessart, Livne & Waldman (2010), we infer an explosion energy range of 2 - 3 x 10$^{51}$ erg and this coupled with the observed width of the forbidden [O I] 6300-6364 {\AA} line at 275 days after the explosion gives an upper limit for the main-sequence (non-rotating, solar metallicity) progenitor mass of 17 M*. Our narrow-band H{\alpha} observation, taken nearly 560 days after the explosion and the presence of an emission kink at zero velocity in the Doppler corrected spectra of SN indicate that the event took place in a low luminosity star forming H II region., Comment: Accepted for publication in MNRAS

We construct integrable pseudopotentials with an arbitrary number of fields in terms of elliptic generalization of hypergeometric functions in several variables. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic type systems. An interesting class of integrable (1+1)-dimensional hydrodynamic type systems is also generated by our pseudopotentials., 19 pages, latex

A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable systems having pseudopotentials with movable singularities is described by a functional equation, which can be solved explicitly. This allows us to construct interesting examples of integrable hydrodynamic systems for arbitrary N., 12 pages, latex

All quasilinear NLS-type systems with fourth order symmetry are listed. Vector generalizations of some of them are constructed. Local master symmetries for several systems from the list are found.

We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree., Comment: 16 pages

A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of the authors. A $5\times 5$ matrix Lax pair for the deformed Kowalewski top is proposed. Also deformations of the two-field Kowalewski gyrostat and the $so(p,q)$ Kowalewski top are found. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian {S}hansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its $3\times 3$ matrix Lax representation is constructed., Comment: 9 pages, LaTeX, with corrections