How to study front travelling wave model?
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To study front traveling wave models, several methods can be used. One approach is to analyze the system using numerical simulations and linear stability analysis to determine the stability and parameter regions where the traveling waves are stable . Another method involves computing the traveling wave fronts using traveling wave equations and solving them as an initial-value problem to obtain accurate wave profiles and speeds . Additionally, a combination of analytical and numerical methods can be employed to study the stability of traveling waves, such as analyzing the spectra of the linearization of the system about the waves . These methods have been applied to various systems, including two-component systems on a one-dimensional lattice , coupled nonlinear oscillators modeling artificial perceptions of light , bacterial colony patterns , thin liquid film flow with surfactants , and electrodeposition experiments .
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| Papers (4) | Insight |
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16 Citations | The paper discusses an analytical and numerical study of a reaction-diffusion system for studying front travelling waves in electrodeposition experiments. |
2 Citations | The paper uses a combination of analytical and numerical methods to study the stability of traveling wave solutions in a model for a surfactant driven flow on an inclined plane. |
5 Citations | The paper uses two methods to study traveling wave fronts: 1) solving the traveling wave equations as an initial-value problem, and 2) solving an initial-moving boundary-value problem for the PDE system. |
84 Citations | The paper discusses the study of traveling front solutions for a two-component system on a one-dimensional lattice. It provides a proof of the existence of traveling fronts and characterizes the minimal wave speed based on the parameters in the system. |
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