scholarly journals Stability of Traveling Waves to a Burgers Equation with 2nd-Order Nonlinear Diffusion

2022 ◽  
Vol 4 (1) ◽  
pp. 77-85
Author(s):  
Mohammad Ghani
Keyword(s):  
Asymptotic Stability ◽  
Small Perturbation ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Nonlinear Diffusion ◽  
Wave Amplitude ◽  
Energy Estimate ◽  
Burgers Equation ◽  
Original Equation ◽  
The Stability

We are interested in the study of asymptotic stability for Burgers equation with second-order nonlinear diffusion. We first transform the original equation by the ansatz transformation to establish the existence of traveling wave. We further employ the energy estimate under small perturbation and arbitrary wave amplitude. This energy estimate is then used to establish the stability.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

scholarly journals Synaptic propagation in neuronal networks with finite-support space dependent coupling

2020 ◽  
Author(s):  
Ricardo Erazo Toscano ◽  
Remus Osan
Keyword(s):  
Time Constant ◽  
Sensory Processing ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Neuronal Networks ◽  
Evolution Equations ◽  
Network Connectivity ◽  
Space Constant ◽  
The Stability ◽  
The Brain

1AbstractTraveling waves of electrical activity are ubiquitous in biological neuronal networks. Traveling waves in the brain are associated with sensory processing, phase coding, and sleep. The neuron and network parameters that determine traveling waves’ evolution are synaptic space constant, synaptic conductance, membrane time constant, and synaptic decay time constant. We used an abstract neuron model to investigate the propagation characteristics of traveling wave activity. We formulated a set of evolution equations based on the network connectivity parameters. We numerically investigated the stability of the traveling wave propagation with a series of perturbations with biological relevance.

ABUNDANCE OF TRAVELING WAVES IN COUPLED CIRCLE MAPS

2000 ◽  
Vol 10 (09) ◽  
pp. 2061-2073 ◽  
Author(s):  
WEN-XIN QIN
Keyword(s):  
Fixed Point ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Initial Conditions ◽  
Periodic Structures ◽  
Time Evolution Operator ◽  
Circle Maps ◽  
Temporal Complexity ◽  
Spatial Periodicity ◽  
The Stability

In this paper we study the existence of traveling waves with any rational velocity in coupled circle maps. We introduce an induced map, then a traveling wave with velocity p/q corresponds to a fixed point of the induced map. Moreover, the stability of a traveling wave is equivalent to that of the corresponding fixed point. Space translational system is chaotic on the set of traveling waves with rational velocities. In addition, time evolution operator exhibits sensitivity-like behavior with respect to initial conditions. By investigating the spatial periodicity of traveling waves, we obtain infinitely many space-time periodic structures. We also consider spatial asymptoticity of these traveling waves, which leads to the existence of fronts, defect solutions and soliton-like solutions. The abundance of traveling waves may be regarded as a signature of the spatial-temporal complexity in extended systems.

scholarly journals Nonlinear Stability of Periodic Traveling Wave Solutions for(n +1)-Dimensional Coupled Nonlinear Klein-Gordon Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Cong Sun ◽  
Bo Jiang
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Orbital Stability ◽  
Traveling Wave Solutions ◽  
Optical Fiber Communication ◽  
Fiber Communication ◽  
Periodic Traveling Waves ◽  
Klein Gordon ◽  
Periodic Traveling Wave ◽  
The Stability

We study the existence and orbital stability of smooth periodic traveling waves solutions of the(n +1)-dimensional coupled nonlinear Klein-Gordon equations. Such a system occurs in quantum mechanics, fluid mechanics, and optical fiber communication. Inspired by Angulo Pava’s results (2007), and by applying the stability theory established by Grillakis et al. (1987), we prove the existence of periodic traveling waves solutions and obtain the orbital stability of the solutions to this system.

scholarly journals Stability of Traveling Waves to the Lotka-Volterra Competition Model

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Ahmad Alhasanat ◽  
Chunhua Ou
Keyword(s):  
Global Stability ◽  
Comparison Principle ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Functional Space ◽  
Cooperative System ◽  
Wave Solutions ◽  
Diffusive Model ◽  
The Stability

In this paper, the stability of traveling wave solutions to the Lotka-Volterra diffusive model is investigated. First, we convert the model into a cooperative system by a special transformation. The local and the global stability of the traveling wavefronts are studied in a weighted functional space. For the global stability, comparison principle together with the squeezing technique is applied to derive the main results.

NONLINEAR STABILITY OF LARGE AMPLITUDE VISCOUS SHOCK WAVES OF A GENERALIZED HYPERBOLIC–PARABOLIC SYSTEM ARISING IN CHEMOTAXIS

2010 ◽  
Vol 20 (11) ◽  
pp. 1967-1998 ◽  
Author(s):  
TONG LI ◽  
ZHI-AN WANG
Keyword(s):  
Nonlinear Stability ◽  
Parabolic System ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Band ◽  
Nonlinear Kinetics ◽  
Diffusive Limit ◽  
Viscous Shock Waves ◽  
The Stability

Traveling wave (band) behavior driven by chemotaxis was observed experimentally by Adler1,2 and was modeled by Keller and Segel.15 For a quasilinear hyperbolic–parabolic system that arises as a non-diffusive limit of the Keller–Segel model with nonlinear kinetics, we establish the existence and nonlinear stability of traveling wave solutions with large amplitudes. The numerical simulations are performed to show the stability of the traveling waves under various perturbations.

An Approach of Wavefront Identification for Traveling Wave Fault Location Based on Harris Corner Detector

2014 ◽  
Vol 960-961 ◽  
pp. 1100-1103
Author(s):  
Guang Bin Zhang ◽  
Hong Chun Shu ◽  
Ji Lai Yu
Keyword(s):  
Traveling Waves ◽  
Transmission Lines ◽  
Traveling Wave ◽  
Fault Location ◽  
Corner Point ◽  
Harris Corner ◽  
Corner Points ◽  
Simulated Test ◽  
Harris Corner Detector ◽  
Calculated Distance

Wavefront identification is important for traveling based fault location. In order to improve its reliability, a novel wavefront identification method based on Harris corner detector has been proposed in this paper. The principle of single-ended traveling wave fault location was briefly introduced at first, and the features of wavefronts generated by faults on transmission lines were analyzed. The arrival of traveling waves' wavefronts is considered as corner points in digital image of waveshape. The corner points can be extracted precisely by Harris corner detector, and both false corner points and non-fault caused disturbance can be eliminated according to the calculated distance between two neighbour corner points and the angle of the corner point. The proposed method is proved feasible and effective by digital simulated test.

scholarly journals The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan Balint ◽  
Agneta M. Balint
Keyword(s):  
Euler Equation ◽  
Function Space ◽  
Euler Equations ◽  
Small Perturbation ◽  
Function Spaces ◽  
Well Posedness ◽  
Small Solution ◽  
Null Solution ◽  
Linearized Euler Equations ◽  
The Stability

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.

Application of projection-based model reduction to finite-element plate models for two-dimensional traveling waves

2016 ◽  
Vol 28 (14) ◽  
pp. 1886-1904 ◽  
Author(s):  
Vijaya VN Sriram Malladi ◽  
Mohammad I Albakri ◽  
Serkan Gugercin ◽  
Pablo A Tarazaga
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Traveling Waves ◽  
Large Scale ◽  
Fe Model ◽  
Plate Model ◽  
Reduction Techniques ◽  
State Frequency ◽  
Scale Down ◽  
The Stability

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results.

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