BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Counting unstable eigenvalues in Hamiltonian spectral problems via commuting operators Haragus, Mariana


We present a general counting result for the unstable eigenvalues of linear operators of the form JL in which J and L are skew- and self-adjoint operators, respectively. Assuming that there exists a self-adjoint operator K such that the operators JL and JK commute, we prove that the number of unstable eigenvalues of JL is bounded by the number of nonpositive eigenvalues of K. As an application, we discuss the transverse stability of one-dimensional periodic traveling waves in the classical KP-II (Kadomtsev-Petviashvili) equation.

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