与KDV相关方程的解析解(英文)

自从孤立波发现以来．KDV方程作为一个典型的非线性与色散平衡模型就出现在流体力学、大气科学、空间等离子体物理等领域，它也是非线性科学中谈论较多的模型。故此，关于它的研究广泛而深入，仅其解析研究就有大量工作。本文对有关KDV方程的解析研究结果给予了总结，并对一般高阶色散情况给出了求解公式。

Reviews on Analytical Solutions to the KDV Related Equations

Since the publicity of so1iton theory, the famous KDV equation, as a typical model de-scribing the balance between nonlinearity and dispersion, has appeared in various fields suchas fluid mechanics, atmospheric 5cience, space plasma physics; its study is also a hot topic intoday's nonlinear science. Therefore, both quantitative and qualitative studies for the KDVrelated equations have been made extensively and deeply; to be specific, there are a largeamount of analytical works devoted to the KDV related equations- The aim of the presentpaper is to review the existing results on this topic and give a general solution formu1ation forthe KDV equations with higher dispersions.