长水波近似方程组的新精确解  

New Exact Solutions of the Approximate Equations for Long Water Waves

作　　者：田贵辰[1] 刘希强[2] 

机构地区：[1]石家庄师范专科学校数学系,河北石家庄050801 [2]聊城大学数学学院,山东聊城252059

出　　处：《数学的实践与认识》2005年第3期105-110,共6页Mathematics in Practice and Theory

基　　金：山东省自然科学基金资助课题 (No.2 0 0 4z X1 6)

摘　　要：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 .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.

关 键 词：齐次平衡法 长水波方程组 精确解 非线性发展方程 偏微分 

分 类 号：O175[理学—数学]