The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

中文翻译：

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一些非线性波动方程的流氓波和同宿解的孪生性质

在Hirota双线性方法的基础上，提出了参数限制法来构造非线性偏微分方程(NLPDEs)的流氓波解。一些实数和复数微分方程作为具体例子来说明所描述方法的有效性和正确性。分别通过三维图形获得并模拟了不同结构的流氓波和同宿解。更重要的是，我们发现流氓波解和同宿解是成对出现的。也就是说，对于一些NLPDEs，如果有同宿解，那么必然有流氓波解。讨论了一类 NLPDE 的流氓波解和同宿解的孪生现象。