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A. V. Yurov

Publications and source records attributed to A. V. Yurov.

32 records · Page 2Linked to original sources
arXiv2005

BLP dissipative structures in plane

We study the Darboux and Laplace transformations for the Boiti-Leon-Pempinelli equations (BLP). These equations are the (1+2) generalization of the sinh-Gordon equation. In addition, the BLP equations reduced to the Burgers (and anti-Burgers) equation in a one-dimensional limit. Localized nonsingular solutions in both spatial dimensions and (anti) "blow-up" solutions are constructed. The Burgers equation's "dressing" procedure is suggested. This procedure allows us to construct such solutions of the BLP equations which are reduced to the solutions of the dissipative Burgers equations when $t\to \infty$. These solutions we call the BLP dissipative structures.

nlin.SI↗
arXiv2005

The nonsingular brane solutions via the Darboux transformation

We consider the Darboux transformation as a method of construction of exact nonsingular solutions describing the three-dimensional brane that interacts with five-dimensional gravity and the bulk scalar field. To make it work, the five-dimensional Einstein's equations and the Israel's conditions are being reduced to the Schrödinger equation with the jump-like potential and the wave functions sewing conditions in jump point correspondingly. We show further that it is always possible to choose the functions in Crum's determinants in such way, that the five-dimensional Ricci scalar $R$ will always be finite both on brane and in bulk. The new exact solutions being the generalizations of the model with the odd superpotential are presented. Described formalism is also appliable to the cases of more realistic branes with cosmological expansion. As an example, via the usage of the simple orbifold model ($S_1/{\Bbb Z}_2$) and one-time Darboux transformation we construct the models where the cosmological constant on the visible brane is exponentially small.

hep-th↗
arXiv2005

Can we escape from the big rip in the achronal cosmic future?

Recently Pedro F. Gonzalez-Diaz had shown that phantom energy can results in achronal cosmic future where the wormholes become infinite before the occurrence of the big rip singularity. After that, while the phantom energy continues its accretion, any wormhole becomes the Einstein-Rosen bridge. Pedro F. Gonzalez-Diaz has suggested that such objects can be used by an advanced civilization as the means of escape from the big rip. Using the Bekenstein Bound we'll show that it is impossible due to the very strong upper bound laid on the total amount of information which can be sent through this bridge.

astro-ph↗
arXiv2005

The Darboux Transformation and Exactly Solvable Cosmological Models

We present a simple and effective method for constructing exactly solvable cosmological models containing inflation with exit. This method does not involve any parameter fitting. We discuss the problems arising with solutions that violate the weak energy condition.

hep-th↗
arXiv2005

Quantum cosmologies with varying speed of light and the $Λ$ problem

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. For the universe filled with a vacuum of constant energy density the semiclassical tunneling nucleation probability can be estimated as $\emph{P}\sim\exp(-α^2/Λ)$ where $α$=const and $Λ$ is the cosmological constant, so once it nucleates, the universe immediately starts the de Sitter inflationary expansion. The probability $\emph{P} $ will be large for values of $Λ$ that are large enough, whereas $Λ$ of our Universe is definitely small. Of course, for the early universe filled with radiation or another ''matter'' the mentioned probability is large nevertheless ($\emph{P}\sim 1$) but in this case we have no inflation which is a standard solution for the flatness and horizon problems. In the other hand, the alternative solution of these problems can be obtained in framework of cosmologies with varying speed of light $c(t)$ (VSL). We show that, as a matter of principle, such quantum VSL cosmologies exist that $\emph{P}\sim 1$, $ρ_{_Λ}/ρ_c\sim 0.7$ ($Λ$-problem) and both horizon and flatness problems are solvable without inflation.

hep-th↗
arXiv2004

A new integrable 3+1 dimensional generalization of the Burgers equation

A new nonlinear 3+1 dimensional evolution equation admitting the Lax pair is presented. In the case of one spatial dimension, the equation reduces to the Burgers equation. A method of construction of exact solutions, based on a class of discrete symmetries of the former equation is developed. These symmetries reduce to the Cole-Hopf transformation in one-dimensional limit. Some exact solutions are analyzed, in the physical context of spatial dissipative structures and shock wave dressing.

nlin.SI↗
arXiv2004

The semiclassical tunneling probability in quantum cosmologies with varying speed of light

In quantum cosmology the closed universe can spontaneously nucleate out of the state with no classical space and time. The semiclassical tunneling nucleation probability can be estimated as $\emph{P}\sim\exp(-α^2/Λ)$ where $α$=const and $Λ$ is the cosmological constant. In classical cosmology with varying speed of light c(t) (VSL) it is possible to solve the horizon problem, the flatness problem and the $Λ$-problem if c=sa^n with s=const and n<-2. We show that in VSL quantum cosmology with n<-2 the semiclassical tunneling nucleation probability is $\emph{P}\sim\exp(-β^2Λ^k)$ with beta=const and k>0. Thus, the semiclassical tunneling nucleation probability in VSL quantum cosmology is very different from this one in quantum cosmology with c=const. In particular, this one is strongly suppressed for large values of $Λ$.

hep-th↗
arXiv2004

Brane World Models And Darboux Transformations

We consider a 5-D gravity plus a bulk scalar field, and with a 3-brane. The Darboux transformation is used to construct some exact solutions. To do this we reduce the system of equations, which describes the 5-D gravity and bulk scalar field to the Schrödinger equation. The jump conditions at the branes lead to the jump potential in the Schrödinger equation. Using the Darboux transformation with these jump conditions, we offer a new exact solution of the brane equations, which represents a generalization of the Rundall-Sundrum solution. For simplicity, the main attention is focused on the case when Hubble root on the visible brane is zero. However, the argument is given that our method is valid in more realistic models with cosmological expansion.

hep-th↗
arXiv2003

Closed dressing chains of D=1 and D=2 Toda lattice

We apply the method of dressing chains to reproduction of Toda lattice in the case of D=1 and D=2. On the example of modified equations $m_0TL$ and $m_1TL$ it is shown that combination of the Darboux and Schlesinger transformations results in closed dressing chains.

nlin.SI↗
arXiv2003

The Gödelizing Quantum-Mechanical Automata

Using Albert results we argue that we don't need new physics to understand Gödelization. Albert quantum automaton can "understand" both a formal system and a Gödel proposition which can't be obtained within this system. There are two significant conclusions. The first speaks "against Penrose" whereas the second speaks for him.

quant-ph↗
arXiv2002

Darboux transformation for classical acoustic spectral problem

We study discrete isospectral symmetries for the classical acoustic spectral problem in spatial dimensions one and two, by developing a Darboux (Moutard) transformation formalism for this problem. The procedure follows the steps, similar to those for the Schrödinger operator. However, there is no one-to-one correspondence between the two problems. The technique developed enables one to construct new families of integrable potentials for the acoustic problem, in addition to those already known. The acoustic problem produces a non-linear Harry Dym PDE. Using the technique, we reproduce a pair of simple soliton solutions of this equation. These solutions are further used to construct a new positon solution for this PDE. Furthermore, using the dressing chain approach, we build a modified Harry Dym equation together with its LA-pair. As an application, we construct some singular and non-singular integrable potentials (dielectric permitivity) for the Maxwell equations in a 2D inhomogeneous medium.

nlin.SI↗
arXiv2002

Complex field as inflaton and quintessence

We investigate cosmology with complex scalar field. It is shown that such models can describe two stages of inflation and the oscillatory regime. Thus we don't need both quintessence and $Λ$-term. It is enough to have single complex field to obtain both inflation and present accelerated universe. If the present accelerated expansion was created by the complex field then universe must escape eternal acceleration. Besides, we will show that cosmological equations with complex field admit stationary solution without any cosmological constant.

hep-th↗
arXiv2002

Tachyonic Instability and Darboux Transformation

Using Darboux transformation one can construct infinite family of potentials which lead to the flat spectrum of scalar field fluctuations with arbitrary multiple precision, and, at the same time, with "essentially blue" spectrum of perturbations of metric. Besides, we describe reconstruction problem: find classical potential V(phi) starting from the known "one-loop potential" u(t) = d^2V(phi(t))/d phi(t)^2.

hep-th↗