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Related Experiment Video

Updated: Feb 13, 2026

Analysis of Zebrafish Larvae Skeletal Muscle Integrity with Evans Blue Dye
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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.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 7, 2018
PubMed
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.

Keywords:
Evans functionstabilitytravelling waves

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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.