Related papers: Integrable Anisotropic Evolution Equations on a Sp…
Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative B\"acklund chart, generalizing results in [Fuchssteiner B., Carillo S.,…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The…
We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type $\Delta \vec{N} + \lambda…
It is shown that like Bianchi I, V and IX models, a Kantowski-Sachs cosmological model also allows a unitary evolution on quantization. It has also been shown that this unitarity is not at the expense of the anisotropy. Non-unitarity, if…
We have formulated a kinetic theory for a condensed atomic gas in a trap, i.e., a generalized Gross-Pitaevskii equation, as well as a quantum-Boltzmann equation for the normal and anomalous fluctuations [R. Walser et al., Phys. Rev. A, 59,…
This paper is concerned with non-symplectic involutions of irreducible symplectic manifolds of $K3^{[n]}$-type. We will give a criterion for deformation equivalence and use this to give a lattice-theoretic description of all deformation…
We prove by methods of harmonic analysis a result on existence of solutions for twisted cohomological equations on translation surfaces with loss of derivatives at most 3+ in Sobolev spaces. As a consequence we prove that product…
All non-equivalent integrable evolution equations of third order of the form $u_t=D_x\frac{\delta H}{\delta u}$ are found.
Recent investigation of locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the…
We consider a broad class of static, spherically symmetric generalized Schwarzschild-like solutions with multiple non-interacting anisotropic fluid sources and derive the coordinate transformation from Schwarzschild-like (curvature) to…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
Global deformations of surfaces, immersed into the Euclidean 3-space, by using the modified Novikov--Veselov equation are investigated. relation to the theory of the Willmore functional is discussed
All axisymmetric solutions to the near-horizon geometry equation with a cosmological constant defined on a topological $2$-sphere were derived. The regularity conditions preventing cone singularity at the poles were accounted for. The…
In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of integrable discrete autonomous equations on a square lattice with a non-standard structure of generalized symmetries is constructed. We build modified series by…
Binary symmetry constraints are applied to constructing B\"acklund transformations of soliton systems, both continuous and discrete. Construction of solutions to soliton systems is split into finding solutions to lower-dimensional Liouville…
We study the GMGHS spacetimes to analyze the evolution of the anisotropy universe, which can be treated as a doubly warped products manifold possessing warping functions (or scale factor) having the Kantowski-Sachs solution which represents…
We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial…
In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent…
We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b)…
We study a general linear parabolic problem for Petrovskii parabolic differential system in Sobolev anisotropic distribution spaces of generalized smoothness. Slowly varying functions are used to characterize supplementary generalized…