General rogue waves in the three-wave resonant interaction systems

Abstract General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions divided into three families, which correspond to a simple root, two roots and double root of certain quartic equation arising from dimension reduction, respectively. It is shown that while first family associated with exists for all signs nonlinear coefficients equations, other families can only exist so-called soliton-exchange case, where have signs. Many these wave solutions, such as those roots, ones generated $2\times 2$ block determinant double-root higher-order new not been reported before. Technically, our derivation case achieved generalization previous reduction procedure method, this generalized allows us treat arbitrary multiplicities. Dynamics also examined, patterns presented. Connection between earlier Darboux transformation explained.