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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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2016

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Online Access:  https://hdl.handle.net/2134/22790 
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_version_  1805991330111815680 

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 finiteband, 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 finiteband 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  rrarticle9387434 
institution  Loughborough University 
publishDate  2016 
record_format  Figshare 
spelling  rrarticle938743420161001T00:00:00Z 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 finiteband, 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 finiteband 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. 20161001T00:00:00Z 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 BYNCND 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 