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

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Abstract

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 constant background 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 rogue waves. 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.

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Acknowledgements

This work was supported by the Shandong Provincial Natural Science Foundation (Grant No. ZR2015PD009), the National Natural Science Foundation of China (Grant No. 41506037), and the National Key Research and Development Programme of China (Grant Nos 2016YFC1402000, 2016YFC1402304).

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Authors and Affiliations

  1. College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao , 266100, People’s Republic of China

    Baonan Sun

  2. Laboratory for Regional Oceanography and Numerical Modeling, Qingdao National Laboratory for Marine Science and Technology, Qingdao , 266000, People’s Republic of China

    Baonan Sun & Zhan Lian

  3. Key Laboratory of Marine Science and Numerical Modeling, The First Institute of Oceanography, State Oceanic Administration, Qingdao , 266061, People’s Republic of China

    Baonan Sun & Zhan Lian

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  1. Baonan Sun
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  2. Zhan Lian
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Correspondence to Baonan Sun.

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Sun, B., Lian, Z. Rogue waves in the multicomponent Mel’nikov system and multicomponent Schrödinger–Boussinesq system. Pramana - J Phys 90, 23 (2018). https://doi.org/10.1007/s12043-017-1512-y

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  • DOI: https://doi.org/10.1007/s12043-017-1512-y

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