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Evans function computation for the stability of travelling waves.
B Barker1, J Humpherys2, G Lyng3
1Department of Mathematics, Brigham Young University, Provo, UT 84602, USA.
Summary
The Evans function is a key tool for analyzing the stability of travelling waves, including multidimensional detonation waves. Computational methods using the Evans function help identify instabilities and understand wave behavior.
Area of Science:
- Nonlinear dynamics
- Fluid mechanics
- Computational mathematics
Background:
- Travelling waves are crucial in various scientific fields.
- Determining the stability of these waves is essential for understanding their behavior.
- The Evans function provides a method for spectral analysis of linearized operators.
Purpose of the Study:
- To review computational aspects of the Evans function.
- To apply the Evans function to analyze multidimensional detonation waves.
- To establish spectral stability and identify bifurcation points of nonlinear waves.
Main Methods:
- Utilizing the Evans function, a Wronskian of decaying solutions.
- Performing spectral analysis of the linearized operator about a travelling wave.
- Applying computational techniques to multidimensional detonation wave models.
Main Results:
- The Evans function computation successfully locates unstable eigenvalues.
- Spectral stability of travelling waves can be established.
- Bifurcation points, indicating loss of stability, are identified.
Conclusions:
- The Evans function is a powerful analytical and computational tool for stability analysis.
- Its application to multidimensional detonation waves provides valuable insights.
- This method aids in understanding the behavior and limitations of nonlinear waves.
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