NDLI: Singularity/scattering alternative for a discrete family of static critical solutions with various numbers of unstable eigenmodes

Please wait, while we are loading the content...

Mathematical Models and Computer Simulations : Volume 9

Mathematical Models and Computer Simulations : Volume 8

Mathematical Models and Computer Simulations : Volume 7

Mathematical Models and Computer Simulations : Volume 6

Mathematical Models and Computer Simulations : Volume 5

Mathematical Models and Computer Simulations : Volume 4

Mathematical Models and Computer Simulations : Volume 3

Mathematical Models and Computer Simulations : Volume 3, Issue 6, December 2011

Mathematical Models and Computer Simulations : Volume 3, Issue 5, October 2011

Mathematical Models and Computer Simulations : Volume 3, Issue 4, August 2011

Mathematical Models and Computer Simulations : Volume 3, Issue 3, June 2011

Mathematical Models and Computer Simulations : Volume 3, Issue 2, April 2011

Integral characteristics of genetic code

Generalized Buckley-Leverett problem

Numeric simulation of the formation of hexagonal nanoscale structure arrays in anodic aluminum oxide

Front formation and dynamics in one reaction-diffusion-advection model

Singularity/scattering alternative for a discrete family of static critical solutions with various numbers of unstable eigenmodes

Direct numerical simulation of turbulent flows in fuel rod bundles

Numerical simulation of seismic responses in multilayer geologic media by the grid-characteristic method

Numerical simulation of hypersonic flows around space vehicles descending in the Martian atmosphere

On the necessity of having a correct model of heat release in simulating the multifront structure of a detonation wave

Thermocapillary mechanism of deep penetration in laser beam welding

On calculating the electric potential for 2D silicon transistor with a silicon oxide nanochannel

Asymptotic model of a thin shock layer near a wedge/cone for the Burnett approximation

Comparison of some methods for solving the internal wave propagation problem in a weakly stratified fluid

Mathematical Models and Computer Simulations : Volume 3, Issue 1, February 2011

Mathematical Models and Computer Simulations : Volume 2

Mathematical Models and Computer Simulations : Volume 1

Singularity/scattering alternative for a discrete family of static critical solutions with various numbers of unstable eigenmodes

Content Provider	Springer Nature Link
Author	Donets, E. E. Ayryan, E. A. Streltsova, O. I.
Copyright Year	2011
Abstract	This paper reports on the study of some solutions for a system of coupled nonlinear wave equations of a hyperbolic type, effectively dependent on one spatial (radial) variable and one time variable. This system of equations, which is a coupled system of the Yang-Mills equations with a scalar field, i.e., dilaton, belongs to the so-called class of supercritical systems, for which there exist solutions that inevitably lead to the formation of singularities at a point or even a whole region during a finite period of time at smooth initial distributions with finite energy. This system of equations has regular stationary solutions with finite energy. All such stationary solutions are unstable and can be parametrized by the number N, which is the number of their unstable eigenmodes in linear approximation, and N = 1, 2, 3, …, ∞. The self-consistent problem of the decay of such stationary solutions with N = 1, 2, 3, 4 on the independent excitation of their unstable eigenmodes was solved numerically in nonlinear regime. The corresponding initial-boundary problem was investigated numerically by means of an adaptive computation scheme based on a conservative finite-differential scheme with energy conservation. It has been found that for each considered stationary solution only the perturbation of its basic unstable eigenmode leads to the formation of the singularity/scattering alternative, the governing parameter in the choice of the alternative being the sign of the major unstable eigenmode. It is shown that the independent perturbation of all higher unstable eigenmodes necessarily leads to the formation of a singularity. It is also found that the nonlinear waves formed with the decay of the basic N = 1 solution on the perturbation of its single unstable mode may expose some properties peculiar to solitons.
Starting Page	165
Ending Page	184
Page Count	20
File Format	PDF
ISSN	20700482
Journal	Mathematical Models and Computer Simulations
Volume Number	3
Issue Number	2
e-ISSN	20700490
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-04-06
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	nonlinear wave equations formation of a singularity self-similar solutions Simulation and Modeling Mathematical Modeling and Industrial Mathematics
Content Type	Text
Resource Type	Article
Subject	Modeling and Simulation Computational Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Blowup/scattering alternative for a discrete family of static critical solutions with various number of unstable eigenmodes

Self-similar Solutions Of Nonlinear Wave Equations

On solutions of quasilinear wave equations with nonlinear damping terms

Scattering Theory and Self-Similar Solutions for the Nonlinear Schrdinger Equation

Investigating the Spectrum of Self-Similar Solutions of the Nonlinear Heat Equation

Homotopy Analysis Method for Time-Fractional Wave-Like Equations

Large mass self-similar solutions of the parabolic–parabolic Keller–Segel model of chemotaxis

On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type

Numerical methods of Lagrangian points and particles for one-dimensional wave gas-dynamics equations

Singularity/scattering alternative for a discrete family of static critical solutions with various numbers of unstable eigenmodes

Similar Documents

Blowup/scattering alternative for a discrete family of static critical solutions with various number of unstable eigenmodes

Self-similar Solutions Of Nonlinear Wave Equations

On solutions of quasilinear wave equations with nonlinear damping terms

Scattering Theory and Self-Similar Solutions for the Nonlinear Schrdinger Equation

Investigating the Spectrum of Self-Similar Solutions of the Nonlinear Heat Equation

Homotopy Analysis Method for Time-Fractional Wave-Like Equations

Large mass self-similar solutions of the parabolic–parabolic Keller–Segel model of chemotaxis

On the Existence of Solutions for Some Nondegenerate Nonlinear Wave Equations of Kirchhoff Type

Numerical methods of Lagrangian points and particles for one-dimensional wave gas-dynamics equations

Singularity/scattering alternative for a discrete family of static critical solutions with various numbers of unstable eigenmodes