Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures
We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phy...
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| Format: | Article |
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American Physical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/40683/ |
| _version_ | 1848796114948456448 |
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| author | Gnutzmann, Sven Waltner, Daniel |
| author_facet | Gnutzmann, Sven Waltner, Daniel |
| author_sort | Gnutzmann, Sven |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016)]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs. |
| first_indexed | 2025-11-14T19:42:51Z |
| format | Article |
| id | nottingham-40683 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:42:51Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-406832020-05-04T18:24:45Z https://eprints.nottingham.ac.uk/40683/ Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures Gnutzmann, Sven Waltner, Daniel We consider exact and asymptotic solutions of the stationary cubic nonlinear Schrödinger equation on metric graphs. We focus on some basic example graphs. The asymptotic solutions are obtained using the canonical perturbation formalism developed in our earlier paper [S. Gnutzmann and D. Waltner, Phys. Rev. E 93, 032204 (2016)]. For closed example graphs (interval, ring, star graph, tadpole graph), we calculate spectral curves and show how the description of spectra reduces to known characteristic functions of linear quantum graphs in the low-intensity limit. Analogously for open examples, we show how nonlinear scattering of stationary waves arises and how it reduces to known linear scattering amplitudes at low intensities. In the short-wavelength asymptotics we discuss how genuine nonlinear effects may be described using the leading order of canonical perturbation theory: bifurcation of spectral curves (and the corresponding solutions) in closed graphs and multistability in open graphs. American Physical Society 2016-12-22 Article PeerReviewed Gnutzmann, Sven and Waltner, Daniel (2016) Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures. Physical Review E, 94 (6). 062216/1-062216/19. ISSN 1539-3755 quantum graphs nonlinear waves http://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.062216 doi:10.1103/PhysRevE.94.062216 doi:10.1103/PhysRevE.94.062216 |
| spellingShingle | quantum graphs nonlinear waves Gnutzmann, Sven Waltner, Daniel Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures |
| title | Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures |
| title_full | Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures |
| title_fullStr | Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures |
| title_full_unstemmed | Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures |
| title_short | Stationary waves on nonlinear quantum graphs. II. Application of canonical perturbation theory in basic graph structures |
| title_sort | stationary waves on nonlinear quantum graphs. ii. application of canonical perturbation theory in basic graph structures |
| topic | quantum graphs nonlinear waves |
| url | https://eprints.nottingham.ac.uk/40683/ https://eprints.nottingham.ac.uk/40683/ https://eprints.nottingham.ac.uk/40683/ |