Rogue waves and solitons on a cnoidal background
Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia
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Received: 11 September 2013
Revised: 25 November 2013
Published online: 23 January 2014
Solutions of the nonlinear Schrödinger equation, appearing as rogue waves on a spatially-periodic background envelope, are obtained using the Darboux transformation scheme. Several particular examples are illustrated numerically. These include soliton and breather solutions on a periodic background as well as higher-order structures. The results enrich our knowledge of possible analytic solutions that describe the appearance of rogue waves in a variety of situations.
This work is prepared on the occasion of Prof. Helmut Brand's 60th birthday. He has made significant contributions to the science of solitons and his ideas have inspired our research into localised formations in various physical contexts.
© EDP Sciences, Springer-Verlag, 2014