We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.

翻译：我们研究了非线性分散波方程式单波溶液中的数字错误。一些关于特定方程式单波溶液离散的现有结果显示,对于不节能、而仅为保守方法直线增长的数字方法来说,错误在时间上是二次增长的。我们提供的数字实验表明,这一结果延伸到一个非常广泛的方程式和数字方法类别。