On Classification of Integrable Davey-Stewartson Type Equations

This paper is devoted to the classification of integrable Davey-Stewartson type equations. A list of potentially deformable dispersionless systems is obtained through the requirement that such systems must be generated by a polynomial dispersionless Lax pair. A perturbative approach based on the method of hydrodynamic reductions is employed to recover the integrable systems along with their Lax pairs. Some of the found systems seem to be new

Development of a Gd Loaded Liquid Scintillator for Electron Anti-Neutrino Spectroscopy

We report on the development and deployment of 11.3 tons of 0.1% Gd loaded liquid scintillator used in the Palo Verde reactor neutrino oscillation experiment. We discuss the chemical composition, properties, and stability of the scintillator elaborating on the details of the scintillator preparation crucial for obtaining a good scintillator quality and stability.Comment: 9 pages, 4 figures, submitted to NIM

On a class of integrable systems of Monge-Amp\`ere type

We investigate a class of multi-dimensional two-component systems of Monge-Amp\`ere type that can be viewed as generalisations of heavenly-type equations appearing in self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of skew-symmetric matrix pencils, a classification of normal forms of such systems is obtained. All two-component systems of Monge-Amp\`ere type turn out to be integrable, and can be represented as the commutativity conditions of parameter-dependent vector fields. Geometrically, systems of Monge-Amp\`ere type are associated with linear sections of the Grassmannians. This leads to an invariant differential-geometric characterisation of the Monge-Amp\`ere property.Comment: arXiv admin note: text overlap with arXiv:1503.0227

Gravity effects on thick brane formation from scalar field dynamics

The formation of a thick brane in five-dimen\-sional space-time is investigated when warp geometries of $AdS_5$ type are induced by scalar matter dynamics and triggered by a thin-brane defect. The scalar matter is taken to consist of two fields with $O(2)$ symmetric self interaction and with manifest $O(2)$ symmetry breaking by terms quadratic in fields. One of them serves as a thick brane formation mode around a kink background and another one is of a Higgs-field type which may develop a classical background as well. Scalar matter interacts with gravity in the minimal form and gravity effects on (quasi)localized scalar fluctuations are calculated with usage of gauge invariant variables suitable for perturbation expansion. The calculations are performed in the vicinity of the critical point of spontaneous breaking of the combined parity symmetry where a non-trivial v.e.v. of the Higgs-type scalar field is generated. The nonperturbative discontinuous gravitational effects in the mass spectrum of light localized scalar states are studied in the presence of a thin-brane defect. The thin brane with negative tension happens to be the most curious case when the singular barriers form a potential well with two infinitely tall walls and the discrete spectrum of localized states arises completely isolated from the bulk.Comment: 15 pages, minor corrections, two-column EPJ-C styl

Integrability of Nonabelian Differential-Difference Equations: the Symmetry Approach

We propose a novel approach to tackle integrability problem for evolutionary differential-difference equations (D$\Delta$Es) on free associative algebras, also referred to as nonabelian D$\Delta$Es. This approach enables us to derive necessary integrability conditions, determine the integrability of a given equation, and make progress in the classification of integrable nonabelian D$\Delta$Es. This work involves establishing symbolic representations for the nonabelian difference algebra, difference operators, and formal series, as well as introducing a novel quasi-local extension for the algebra of formal series within the context of symbolic representations. Applying this formalism, we solve the classification problem of integrable skew-symmetric quasi-linear nonabelian equations of orders $(-1,1)$, $(-2,2)$, and $(-3,3)$, consequently revealing some new equations in the process