Work

Spectral analysis for matrix Hamiltonian operators

Year: 2010

Type: article

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. Although 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 computations, and for further experimentation, is available at http://hdl.handle.net/1807/25174 .

Source: Nonlinearity

DOI: 10.1088/0951-7715/24/2/003

Authors: Jeremy L Marzuola, Gideon Simpson

Institutions: University of North Carolina at Chapel Hill, University of Toronto

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2074948932

FWCI: 6.424

Cites: 23

Cited by: 32

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