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Explicit forms of various breathers, including inclined periodic breather, Akhmediev breather, Ma breather and rogue wave solutions, are obtained for the coupled long-wave-short-wave system by using a Hirota two-soliton method with complex frequency and complex wave number. Based on the structures of these breather solutions and figures via computer simulation, the characteristics of various breather solutions are discussed which might provide us with useful information on the dynamics of the relevant physical fields.

Various breathers and rogue waves for the coupled long-wave-short-wave system