3 papers
math.SP2026
Hadamard-type formulas for real eigenvalues of canonically symplectic operators
Mitchell Curran, Selim Sukhtaiev
We give first-order asymptotic expansions for the resolvent and Hadamard-type formulas for the eigenvalue curves of one-parameter families of canonically symplectic operators. We a…
math.SP2024
Detecting eigenvalues in a fourth-order nonlinear Schrödinger equation with a non-regular Maslov box
Mitchell Curran, Robert Marangell
We use the Maslov index to study the eigenvalue problem arising from the linearisation about solitons in the fourth-order cubic nonlinear Schrödinger equation (NLSE). Our analysis…
math.SP2022
Hamiltonian spectral flows, the Maslov index, and the stability of standing waves in the nonlinear Schrödinger equation
Graham Cox, Mitchell Curran, Yuri Latushkin +1
We use the Maslov index to study the spectrum of a class of linear Hamiltonian differential operators. We provide a lower bound on the number of positive real eigenvalues, which in…