| Abstract: |
| In recent work, Baird et al. have introduced a generalized
Maslov index which allows oscillation techniques that have
previously been restricted to eigenvalue problems with
underlying Hamiltonian structure to be extended to the
non-Hamiltonian setting
[T. J. Baird, P. Cornwell, G. Cox, C. Jones, and R. Marangell,
Generalized Maslov indices for non-Hamiltonian systems,
SIAM J. Math. Anal. 54 (2022) 1623-1668].
I will discuss how this approach can be implemented in the
analysis of spectral instability for nonlinear waves,
taking as my setting a class of equations previously
investigated by Pego and Weinstein via the Evans function
[R. L. Pego and M. I. Weinstein,
Eigenvalues, and instabilities of solitary waves,
Phil. Trans. R. Soc. Lond. A 340 (1992) 47-94]. |
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