Spectra of Linearized Operators for NLS Solitary Waves
Shu-Ming Chang, Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai
TL;DR
This paper investigates the spectral properties of linearized operators around solitary waves in focusing NLS equations, linking these spectra to stability and long-term dynamics through analytical and numerical methods.
Contribution
It provides a detailed analysis of the spectra of linearized operators for NLS solitary waves, combining analytical and numerical approaches to enhance understanding.
Findings
Spectral properties are characterized analytically.
Numerical simulations support the analytical findings.
Connections between spectra and stability are clarified.
Abstract
Nonlinear Schr\"odinger (NLS) equations with focusing power nonlinearities have solitary wave solutions. The spectra of the linearized operators around these solitary waves are intimately connected to stability properties of the solitary waves, and to the long-time dynamics of solutions of (NLS). We study these spectra in detail, both analytically and numerically.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Spectral Theory in Mathematical Physics