Rogue waves in the multicomponent Mel’nikov system and multicomponent Schrödinger–Boussinesq system

Pramana: Journal of physics

BAONAN SUN^1,2,3¹  ZHAN LIAN^2,3³ 

[1] College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao 266100, People’s Republic of China^1;Key Laboratory of Marine Science and Numerical Modeling, The First Institute of Oceanography, State Oceanic Administration, Qingdao 266061, People’s Republic of China^3;Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266000, People’s Republic of China^2

关键词: Multicomponent Mel’nikov system;    multicomponent Schrödinger–Boussinesq system;    rogue waves;    bilinear transformation method;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel’nikov equation and the multicomponent Schrödinger–Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel’nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constantbackground with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line roguewaves.Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger–Boussinesq system are generated.

【 授权许可】

CC BY