Abstract We construct numerically solitary wave solutions of the Rosenau equation using the Petviashvili iteration method. We first summarize the theoretical results available in the literature for the existence of solitary wave solutions. We then apply two numerical algorithms based on the Petviashvili method for solving the Rosenau equation with single or double power law nonlinearity. Numerical calculations rely on a uniform discretization of a finite computational domain. Through some numerical experiments we observe that the algorithm converges rapidly and it is robust to very general forms of the initial guess.

中文翻译：

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Rosenau方程孤波解的数值计算

摘要 我们使用 Petviashvili 迭代法构造了 Rosenau 方程的数值孤立波解。我们首先总结了文献中关于孤波解存在的理论结果。然后我们应用两种基于 Petviashvili 方法的数值算法来求解具有单或双幂律非线性的 Rosenau 方程。数值计算依赖于有限计算域的统一离散化。通过一些数值实验，我们观察到该算法收敛速度很快，并且对初始猜测的非常一般形式具有鲁棒性。