SPECTRAL STABILITY OF BI-FREQUENCY SOLITARY WAVES IN SOLER AND DIRAC-KLEIN-GORDON MODELS
| Affiliation auteurs | !!!! Error affiliation !!!! |
| Titre | SPECTRAL STABILITY OF BI-FREQUENCY SOLITARY WAVES IN SOLER AND DIRAC-KLEIN-GORDON MODELS |
| Type de publication | Journal Article |
| Year of Publication | 2018 |
| Auteurs | Boussaid N, Comech A |
| Journal | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS |
| Volume | 17 |
| Pagination | 1331-1347 |
| Date Published | JUL |
| Type of Article | Article |
| ISSN | 1534-0392 |
| Mots-clés | 1) symmetry, Bi-frequency solitary waves, Bogoliubov SU(1, Dirac-Klein-Gordon system, linear instability, nonlinear Dirac equation, qubits, qudits, Soler model, Spectral stability, Yukawa model |
| Résumé | 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 +/- 2 omega i 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. |
| DOI | 10.3934/cpaa.2018065 |