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- Title
SPECTRAL STABILITY OF BI-FREQUENCY SOLITARY WAVES IN SOLER AND DIRAC--KLEIN--GORDON MODELS.
- Authors
Boussïd, Nabile; Comech, Andrew
- Abstract
We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction, known as the Soler model (with an arbitrary nonlinearity and in arbitrary dimension) and the Dirac--Klein--Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of qubit and qudit states in the theory of quantum computing. We show the relation of ±2wi eigenvalues of the linearization at a solitary wave, Bogoliubov SU(1; 1) symmetry, and the existence of bi-frequency solitary waves. We show that the spectral stability of these waves reduces to spectral stability of usual (one-frequency) solitary waves.
- Subjects
SPECTRAL analysis (Phonetics); SOLITONS; DIRAC equation; KLEIN paradox; YUKAWA interactions
- Publication
Communications on Pure & Applied Analysis, 2018, Vol 17, Issue 4, p1331
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2018065