Spectral Analysis for Matrix Hamiltonian Operators

Abstract

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schrödinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.

57 pages, 22 figures, typos fixed

Cited by in corpus (7)

• Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
• On the spectral properties of L_{+-} in three dimensions
• Blow-up dynamics and spectral property in the $L^2$-critical nonlinear Schrödinger equation in high dimensions
• On orbital instability of spectrally stable vortices of the NLS in the plane
• Embedded Eigenvalues and the Nonlinear Schrodinger Equation
• Dispersive Estimates for Scalar and Matrix Schrödinger operators on ${\mathbb{H}}^{n+1}$
• Dispersive estimates for matrix Schrödinger operators in dimension two