6 papers
Stability of Ginzburg-Landau pulses via Fredholm determinants of Birman-Schwinger operators
Erika Gallo, John Zweck, Yuri Latushkin
We introduce a numerical method to determine the stability of stationary pulse solutions of the complex Ginzburg-Landau equation. The method involves the computation of the point s…
Numerical Fredholm determinants for matrix-valued kernels on the real line
Erika Gallo, John Zweck, Yuri Latushkin
We analyze a numerical method for computing Fredholm determinants of trace class and Hilbert Schmidt integral operators defined in terms of matrix-valued kernels on the entire real…
The calculus of Duistermaat's triple index
Gregory Berkolaiko, Graham Cox, Yuri Latushkin +1
In this paper we develop a systematic calculus for the Duistermaat index, a symplectic invariant defined for triples of Lagrangian subspaces. Introduced nearly half a century ago,…
A regularity condition under which integral operators with operator-valued kernels are trace class
John Zweck, Yuri Latushkin, Erika Gallo
We study integral operators on the space of square-integrable functions from a compact set, , to a separable Hilbert space, . The kernel of such an operator takes values in t…
Fredholm determinants, continued fractions, Jost and Evans functions for a Jacobi matrix associated with the 2D-Euler equations
Yuri Latushkin, Shibi Vasudevan
For a second order difference equation that arises in the study of stability of unidirectional (generalized Kolmogorov) flows for the Euler equations of ideal fluids on the two dim…
Stability of fronts in the diffusive Rosenzweig-MacArthur model
Anna Ghazaryan, Stéphane Lafortune, Yuri Latushkin +1
We consider a diffusive Rosenzweig-MacArthur predator-prey model in the situation when the prey diffuses at the rate much smaller than that of the predator. In a certain parameter…