Tensor mode perturbation of cosmology with higher order holonomy corrections

2016 ◽  
Vol 94 (9) ◽  
pp. 945-952
Author(s):  
Yu Li
Keyword(s):  
Wave Equation ◽  
Gravitational Wave ◽  
Quantum Cosmology ◽  
Source Term ◽  
Friedmann Equation ◽  
Mass Term ◽  
Higher Order ◽  
Quantum Corrections ◽  
Tensor Mode ◽  
Higher Order Corrections

In this paper, we discuss the tensor mode perturbation in the frame of loop quantum cosmology with higher order holonomy corrections. We get the dynamics of the background near the bounce and far from the bounce. Based on the solutions of the effective Friedmann equation, we deduce the effective gravitational wave equation and get the quantum corrections in both the mass term and source term. We solve the gravitational wave equation near the bounce and discuss the situation far from the bounce. We also find the new terms arose only when one considers the higher order corrections.

scholarly journals LOW-ENERGY QUANTUM STRING COSMOLOGY

1998 ◽  
Vol 13 (28) ◽  
pp. 4779-4786 ◽  
Author(s):  
MAURIZIO GASPERINI
Keyword(s):  
Nonperturbative Effects ◽  
Effective Action ◽  
Quantum Cosmology ◽  
Higher Order ◽  
String Cosmology ◽  
Low Energy ◽  
Exit Problem ◽  
Energy Quantum ◽  
Higher Order Corrections

We introduce a Wheeler–De Witt approach to quantum cosmology based on the low-energy string effective action, with an effective dilaton potential included to account for nonperturbative effects and, possibly, higher-order corrections. We classify, in particular, four different classes of scattering processes in minisuperspace, and discuss their relevance for the solution of the graceful exit problem.

scholarly journals Higher Order Wave Equation with Logarithmic Source Term

2017 ◽  
Author(s):  
Sh. Hajrulla ◽  
L. Bezati ◽  
F. Hoxha
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Source Term ◽  
Boundary Value ◽  
Initial Boundary ◽  
Global Weak Solution ◽  
Initial Boundary Value Problem ◽  
Logarithmic Sobolev Inequality ◽  
Higher Order ◽  
Initial Boundary Value

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

Exponential Decay of Global Solutions for some Quasilinear Higher-Order Wave Equation

2013 ◽  
Vol 336-338 ◽  
pp. 2233-2237
Author(s):  
Ren Bing Lin
Keyword(s):  
Wave Equation ◽  
Exponential Decay ◽  
Source Term ◽  
Global Solutions ◽  
Higher Order ◽  
Damping Term ◽  
Uniform Stabilization ◽  
Linear Damping

In this paper we prove the uniform stabilization of global solutions for some quasilinear higher-order wave equation with linear damping term and source term by applying a lemma due to V.Komornik.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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