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

中文翻译：

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三波共振交互系统中的一般流氓波

(1+1)维三波谐振相互作用系统中的一般流氓波是通过双线性方法推导出来的。这些解分为三个族，分别对应于降维产生的某个四次方程的一个单根、两个单根和一个双根。结果表明，虽然与单根相关的第一类解存在于三波相互作用方程中非线性系数的所有符号，但与两个单根和双根相关的其他两类解只能存在于所谓的孤子交换情况，其中非线性系数具有一定的符号。许多这些流氓波解决方案，例如与两个简单根相关联的那些，在双根情况下由 $2\times 2$ 块行列式生成的那些，和与简单根相关的高阶解是以前没有报道过的新解。从技术上讲，我们对双根情况下的流氓波的双线性推导是通过对双线性方法中先前的降维过程的泛化来实现的，并且这个泛化过程允许我们处理任意多重性的根。还检查了衍生的流氓波的动力学，并提出了新的流氓波模式。还解释了这些双线性流氓波与较早通过 Darboux 变换得出的波之间的联系。我们对双根情况下的流氓波的双线性推导是通过对双线性方法中先前的降维过程的推广来实现的，并且这个泛化过程允许我们处理任意多重性的根。还检查了衍生的流氓波的动力学，并提出了新的流氓波模式。还解释了这些双线性流氓波与较早通过 Darboux 变换得出的波之间的联系。我们对双根情况下的流氓波的双线性推导是通过对双线性方法中先前的降维过程的推广来实现的，并且这个泛化过程允许我们处理任意多重性的根。还检查了衍生的流氓波的动力学，并提出了新的流氓波模式。还解释了这些双线性流氓波与较早通过 Darboux 变换得出的波之间的联系。