Relative Morse indices, Fredholm indices, and group velocities

Björn Sandstede, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


We discuss Fredholm properties of the linearization of partial differential equations on cylindrical domains about travelling and modulated waves. We show that the Fredholm index of each such linearization is given by a relative Morse index which depends only on the asymptotic coefficients. Several strategies are outlined that help to compute relative Morse indices using crossing numbers of spatial eigenvalues, and the results are applied to prove the existence of small viscous shock waves in hyperbolic conservation laws upon adding small localized time-periodic source terms.

Original languageEnglish (US)
Pages (from-to)139-158
Number of pages20
JournalDiscrete and Continuous Dynamical Systems
Issue number1
StatePublished - Jan 2008


  • Fredholm operator
  • Group velocity
  • Morse index
  • Spatial dynamics


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