相关论文: Renormalization, averaging, conservation laws and …
Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of…
Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is…
We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual…
When working in synchronous gauges, pseudo-tensor conservation laws are often used to set the initial conditions for cosmological scalar perturbations, when those are generated by topological defects which suddenly appear in an up to then…
After introducing gauge-invariant cosmological perturbation theory we give an improved set of governing equations for multiple fluids including energy transfer. Having defined adiabatic and entropic perturbations we derive the…
We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…
Inspired by the general relation between the boundary global symmetry and the bulk gauge symmetry in AdS/CFT, we reformulate the $d+1$ dimensional AdS gravity theory as a $SO(2,d)$ gauge theory. In this formalism, the pull back of the bulk…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. Further, we work within the context of the "two time framework" (TTF) approximation, which…
Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs)…
We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS…
We study the stability of uniformly moving membrane-like objects in seven dimensional Anti-de Sitter space. This is approached by a linear perturbation analysis and a search for growing modes. We examine both analytic and numerical…
We argue that symmetries and conservation laws greatly restrict the form of the terms entering the long wavelength description of growth models exhibiting anomalous roughening. This is exploited to show by dynamic renormalization group…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
In this paper, we construct and analyse the symmetries and conservation laws (conserved densities) of a model of a nonlinear Scrodinger equation with PT-symmetric potentials and inhomogeneity.