Related papers: Dynamical symmetry breaking described by cubic non…
This work presents a novel family of well-balanced numerical schemes for hyperbolic systems of balance laws based on the kinetic relaxation approach. The method begins by transforming the original non-linear system into a linearized kinetic…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These solutions are obtained from critical points of a dual functional and they are weakly localized in space. Our abstract…
In this communication, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the…
We consider Dynamical Supersymmetry Breaking (DSB) in models with classical flat directions. We analyze a number of examples, and develop a systematic approach to determine if classical flat directions are stabilized in the full quantum…
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a…
It is proved that the quantum-mechanical consideration of global breathing of a hedgehog-like field configuration leads to the dynamically stable soliton solutions in the nonlinear sigma-model without the Skyrme term. Such solutions exist…
The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…
Models for dynamical breaking of supersymmetric grand unified theories are presented. The doublet-triplet splitting problem is absent since the Higgs doublet superfields can be identified with the massless mesons of the strong gauge group…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
Computing the exact dynamics of many-body quantum systems becomes intractable as system size grows. Here, we present a symmetry-based method that provides an exponential reduction in the complexity of a broad class of such problems…
Dynamical breaking of supersymmetry was long thought to be an exceptional phenomenon, but recent developments have altered this view. A question of great interest in the current framework is the value of the underlying scale of…
The linear sigma model with pions and sigma coupled to baryons and a (massive) gauge vector meson is considered for the description of a finite baryonic density system. The stability equation for the bound system is studied in the…
On a two-dimensional planar parity-time-($\mathcal{PT}$-)symmetric nonlinear magnetic metamaterial, consisting of split-ring dimers with balanced gain and loss, discrete breather solutions can be found. We extend these studies and by…
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a…
When nonconforming discontinuous Galerkin methods are implemented for hyperbolic equations using quadrature, exponential energy growth can result even when the underlying scheme with exact integration does not support such growth. Using…
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several…
We obtain real-valued, time-periodic and radially symmetric solutions of the cubic Klein-Gordon equation \begin{align} \partial_t^2 U - \Delta U + m^2 U = \Gamma (x) U^3 \quad \text{on } \mathbb{R} \times \mathbb{R}^3, \end{align} which are…
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate…
Higher symmetries in interacting many-body systems often give rise to new phases and unexpected dynamical behavior. Here, we theoretically investigate a variant of the Dicke model with higher-order discrete symmetry, resulting from…