论文标题
三波共振交互系统中的一般流氓波
General rogue waves in the three-wave resonant interaction systems
论文作者
论文摘要
（1+1） - 维三波谐振系统中的一般流氓波是通过双线性方法得出的。这些溶液分为三个家族，它们分别是由降低尺寸降低产生的一个简单根部，两个简单根和一个四分之一方程的双根。结果表明，尽管三波相互作用方程中非线性系数的所有迹象都存在与简单根相关的第一个溶液家族，但其他两个与两个简单根相关的溶液族只能在所谓的soliton-Exchange情况下，在非线性系数的情况下才有某些迹象。这些流氓波解决方案中有许多（例如与两个简单根相关的解决方案以及与简单根相关的高阶溶液）都是以前没有报道的新溶液。从技术上讲，通过对双线性方法中先前的降低过程的概括，我们对双根病例的流氓波的双线性推导是实现的，并且这种通用过程使我们能够处理任意多重性的根。还检查了派生的流氓波的动力学，并提出了新的流氓波模式。这些双线性流氓波与darboux变换较早衍生的波浪之间的联系也解释了。
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 exist 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, 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.
