Related papers: Hamilton-Jacobi method for Domain Walls and Cosmol…
We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and…
We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in…
Hamilton-Jacobi theory for general relativity provides an elegant covariant formulation of the gravitational field. A general `coordinate-free' method of integrating the functional Hamilton-Jacobi equation for gravity and matter is…
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf…
We consider homoclinic solutions for Hamiltonian systems in symplectic Hilbert spaces and generalise spectral flow formulas that were proved by Pejsachowicz and the author in finite dimensions some years ago. Roughly speaking, our main…
In this study, we examine the domain wall within the framework of a cosmological harmonic oscillator. We investigate the interaction between the domain wall and a periodic background field, which can induce perturbations in the oscillatory…
The geometry and morphology of magnetic domain walls (DWs) are closely related to their dynamics when driven by external forces. Under some reliable approximations DWs can be considered self-affine interfaces, so universal laws govern their…
Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a long-wavelength approximation. We examine the non-linear evolution of the inhomogeneities in the dust fluid case and the cosmological constant case. In the case of dust…
We consider a port-Hamiltonian system on a spatial domain $\Omega \subseteq \mathbb{R}^n$ that is bounded with Lipschitz boundary. We show that there is a boundary triple associated to this system. Hence, we can characterize all boundary…
Using harmonic mean curvature flow, we establish a sharp Minkowski type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard 3-manifolds. This inequality also improves the known estimates for total…
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time…
Relativistic domain walls are studied in the framework of a polynomial approximation to the field interpolating between different vacua and forming the domain wall. In this approach we can calculate evolution of a core and of a width of the…
We perform some analytic continuations of the de Sitter thick domain wall solutions obtained in our previous paper hep-th/0201130 in the system of gravity and a scalar field with an axion-like potential. The obtained new solutions represent…
We present a mathematical framework for generating thick domain wall solutions to the coupled Einstein-scalar field equations which are (locally) plane symmetric. This approach leads naturally to two broad classes of wall-like solutions.…
Discrete symmetries are widely imposed in particle theories. It is well-known that the spontaneous breaking of discrete symmetries leads to domain walls. Current studies of domain walls have focused on those from the spontaneous breaking of…
We demonstrate that the evolution of wall-like inhomogeneities in run-away potentials, characteristic of dynamical supersymmetry breaking and moduli stabilisation, is very similar to the evolution of domain wall networks associated with…
We analyze the possibility of constructing supersymmetric curved domain wall solutions in five-dimensional ${\cal N}=2$ gauged supergravity, which are supported by non-constant scalar fields belonging either to vector multiplets only or to…
We study configurations of intersecting domain walls in a Wess-Zumino model with three vacua. We introduce a volume-preserving flow and show that its static solutions are configurations of intersecting domain walls that form double bubbles,…
The Geometry of planar domain walls is studied. It is argued that the planar walls indeed have plane symmetry. In the Minkowski coordinates the walls are mapped into revolution paraboloids.
Stable domain wall (DW) must decay to avoid overclose the Universe. A commonly used solution is to slightly break the PQ symmetry by introducing a bias term in the potential. In this work, we propose an alternative, symmetry-preserving…