摘要
用吴文俊提出的研究数学史的"新方法论"来研究辅助方程法有关的大量文献,总结了辅助方程法的构造性和机械化性两大特点.在此基础上,发挥这两大特点给出了第一种椭圆辅助方程的新解和Backlund变换,构造了非线性发展方程的无穷序列新精确解.其中包括无穷序列光滑孤立子解、无穷序列尖峰孤立子解和无穷序列紧孤立子解.
A new methodology proposed by WU Wen-jun of studying the history of mathematics is applied to research references on the auxiliary equation method and summarize the two characteristics of constructivity and mechanization about the auxiliary equation method.According to this and developing the two characteristics,new solutions and Bcklund transformation of the first kind of elliptic auxiliary equations are presented to construct new infinite sequence exact solutions of nonlinear evolution equations,which include infinite sequence smooth soliton solutions,infinite sequence peak soliton solutions and infinite sequence compact soliton solutions.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第3期339-354,共16页
Journal of Inner Mongolia University：Natural Science Edition
基金
内蒙古自治区高等学校科学研究基金资助项目(NJZZ07031)
内蒙古自治区自然科学基金(2010MS0111)
关键词
新方法论
辅助方程法
BACKLUND变换
非线性发展方程
无穷序列新精确解
new methodology
the auxiliary equation method
Bcklund transformation
nonlinear evolution equation
new infinite sequence exact solution
