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Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration...
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| Main Authors: | , , |
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| Format: | Default Article |
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2016
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| Online Access: | https://hdl.handle.net/2134/22790 |
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| _version_ | 1805991330111815680 |
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| author | Marco Bertola Gennady El Alexander Tovbis |
| author_facet | Marco Bertola Gennady El Alexander Tovbis |
| author_sort | Marco Bertola (7161977) |
| collection | Figshare |
| description | Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalised rogue wave notion then naturally enters as a large amplitude localised coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite band potentials of the fNLS equation that exhibit generalised rogue waves. |
| format | Default Article |
| id | rr-article-9387434 |
| institution | Loughborough University |
| publishDate | 2016 |
| record_format | Figshare |
| spelling | rr-article-93874342016-10-01T00:00:00Z Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation Marco Bertola (7161977) Gennady El (1258536) Alexander Tovbis (7161533) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalised rogue wave notion then naturally enters as a large amplitude localised coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite band potentials of the fNLS equation that exhibit generalised rogue waves. 2016-10-01T00:00:00Z Text Journal contribution 2134/22790 https://figshare.com/articles/journal_contribution/Rogue_waves_in_multiphase_solutions_of_the_focusing_nonlinear_Schr_dinger_equation/9387434 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified Marco Bertola Gennady El Alexander Tovbis Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation |
| title | Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation |
| title_full | Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation |
| title_fullStr | Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation |
| title_full_unstemmed | Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation |
| title_short | Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation |
| title_sort | rogue waves in multiphase solutions of the focusing nonlinear schrödinger equation |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/22790 |