2019/03/18 by Peter Howard, Alim Sukhtayev, Howard, Peter +1
Mathematics · Physics and Astronomy · #34B24 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1903.07583
openalex publication_date 2019/03/18 · openalex created_date 2022/07/24 · openalex updated_date 2026/07/28
We show that for Sturm-Liouville Systems on the half-line [0,\∞), the\nMorse index can be expressed in terms of the Maslov index and an additional\nterm associated with the boundary conditions at x = 0. Relations are given\nboth for the case in which the target Lagrangian subspace is associated with\nthe space of L2 ((0,\∞), \ℂn) solutions to the\nSturm-Liouville System, and the case when the target Lagrangian subspace is\nassociated with the space of solutions satisfying the boundary conditions at x\n= 0. In the former case, a formula of H "ormander's is used to show that the\ntarget space can be replaced with the Dirichlet space, along with additional\nexplicit terms. We illustrate our theory by applying it to an eigenvalue\nproblem that arises when the nonlinear Schr "odinger equation on a star graph\nis linearized about a half-soliton solution.\n