长水波近似方程组的新精确解

依据齐次平衡法的思想 ,首先提出了求非线性发展方程精确解的新思路 ,这种方法通过改变待定函数的次序 ,优势是使求解的复杂计算得到简化 .应用本文的思路 ,可得到某些非线性偏微分方程的新解 .其次我们给出了长水波近似方程组的一些新精确解 ,其中包括椭圆周期解 ,我们推广了有关长波近似方程的已有结果 .

New Exact Solutions of the Approximate Equations for Long Water Waves

On a basis of the homogenous balance method, we present a new idea of finding some exact solutions to nonlinear evolution equations. The advantage of this method is to simplify complex computatoins of finding solutions by exchanging the order of functions to be determined Applying this method, one can look for new solutions of many nonlinear evolution equations. As an example, we obtain some new exact solutions of the approximate equations for long water waves, which include some periodic solutions expressed by elliptic functions. We generalize some results of the approximate equations for long water waves in the past papers.