The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of three different forms are derived. The results depend on some conditions on the speed of the waves with respect to the parameters of the equations. They are discussed for several families of Rosenau equations present in the literature. The analysis is illustrated with a numerical study of generation of approximate solitary-wave profiles from a numerical procedure based on the Petviashvili iteration.

中文翻译：

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关于Rosenau型方程的孤立波解


本文关注的是 Rosenau 型方程的孤立波解的存在性。利用范式理论和集中紧性理论这两种标准理论，导出了三种不同形式的孤立波存在的一些结果。结果取决于波速相对于方程参数的一些条件。它们针对文献中存在的几个罗西瑙方程组进行了讨论。通过基于 Petviashvili 迭代的数值程序生成近似孤立波剖面的数值研究来说明该分析。