Discrete rogue waves of the Ablowitz-Ladik and Hirota equations

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota te...

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Detalles Bibliográficos
Autores: Ankiewicz, A., Akhmediev, N., Soto Crespo, J. M.
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/59701
Acceso en línea:http://hdl.handle.net/10261/59701
Access Level:acceso abierto
Descripción
Sumario:We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation. © 2010 The American Physical Society.

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