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The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
University Faculty Publications and Creative Works
When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part) but also those which are purely imaginary but have negative Krein signature. These latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues; i.e., they are a necessary building block in the mechanism leading to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a general theory for constructing a meromorphic matrix-valued function, the so-called Krein matrix, which has the property of not only locating the unstable …
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan
University Faculty Publications and Creative Works
When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part) but also those which are purely imaginary but have negative Krein signature. These latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues; i.e., they are a necessary building block in the mechanism leading to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a general theory for constructing a meromorphic matrix-valued function, the so-called Krein matrix, which has the property of not only locating the unstable …