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A generically singular type of saddle–node bifurcation that occurs for relativistic shock waves

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2023

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https://doi.org/10.1016/j.physd.2023.133829
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Physica D: Nonlinear Phenomena. Elsevier. 2023, 453, 133829. ISSN 0167-2789. eISSN 1872-8022. Verfügbar unter: doi: 10.1016/j.physd.2023.133829

Zusammenfassung

This paper is concerned with two-parameter families of planar dynamical systems in which a saddle–node bifurcation interacts with a singular perturbation. We identify bifurcation curves along which the non-saddle point switches from node to focus and establish the existence of heteroclinic connections in either case. As an application, the result is used to show the existence of oscillatory shock profiles in a model of relativistic fluid dynamics.

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510 Mathematik

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Saddle-node bifurcation, Singular perturbation, Heteroclinic orbits, Relativistic fluid dynamics, Shock profiles

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ISO 690PELLHAMMER, Valentin, 2023. A generically singular type of saddle–node bifurcation that occurs for relativistic shock waves. In: Physica D: Nonlinear Phenomena. Elsevier. 2023, 453, 133829. ISSN 0167-2789. eISSN 1872-8022. Verfügbar unter: doi: 10.1016/j.physd.2023.133829
BibTex
@article{Pellhammer2023-11gener-75419,
  title={A generically singular type of saddle–node bifurcation that occurs for relativistic shock waves},
  year={2023},
  doi={10.1016/j.physd.2023.133829},
  volume={453},
  issn={0167-2789},
  journal={Physica D: Nonlinear Phenomena},
  author={Pellhammer, Valentin},
  note={Article Number: 133829}
}
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