scholarly journals On the stability of periodic traveling waves for the modified Kawahara equation

2019 ◽  
pp. 1-8
Author(s):  
Gisele Detomazi Almeida ◽  
Fabrício Cristófani ◽  
Fábio Natali
Keyword(s):  
Traveling Waves ◽  
Kawahara Equation ◽  
Periodic Traveling Waves ◽  
The Stability

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.

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.

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.

scholarly journals Stability of periodic traveling waves for complex modified Korteweg–de Vries equation

2010 ◽  
Vol 248 (10) ◽  
pp. 2608-2627 ◽  
Author(s):  
Sevdzhan Hakkaev ◽  
Iliya D. Iliev ◽  
Kiril Kirchev
Keyword(s):  
Traveling Waves ◽  
Vries Equation ◽  
Periodic Traveling Waves ◽  
De Vries

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.

scholarly journals Modified Kawahara equation within a fractional derivative with non-singular kernel

2018 ◽  
Vol 22 (2) ◽  
pp. 789-796 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Water Waves ◽  
Iterative Scheme ◽  
Singular Kernel ◽  
Kawahara Equation ◽  
Long Wavelength ◽  
Exponential Kernel ◽  
The Stability ◽  
Linear Water Waves

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

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