A minimal hyperbolic system for unstable shock waves

Dmitry I. Kabanov, Aslan Kasimov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using accurate shock-fitting methods. The model may be considered as a minimal hyperbolic system with chaotic solutions and can also serve as a stringent numerical test problem for systems of hyperbolic balance laws.

Original languageEnglish (US)
Pages (from-to)282-301
Number of pages20
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - May 2019
Externally publishedYes


  • Bifurcations
  • Chaos
  • Detonation
  • Hyperbolic systems
  • Shock waves
  • Stability

ASJC Scopus subject areas

  • Applied Mathematics
  • Numerical Analysis
  • Modeling and Simulation


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