Can nth-order nonlinear differential equation be replaced by infinite number of kth-order linear differential equations with n≠k?
We illustrate that, by means of an analytic technique for strongly nonlinear problems, namely the homotopy analysis method, a nth-order nonlinear differential equation might be replaced by an infinite number of kth-order linear differential equations, where k is unnecessary to be equal to n. This tact indicates that we have much larger freedpm to solve nonlinear problems than we traditionally thought. Using this kind of freedom, it might become much easier to solve some nonlinear problems, as illustrated in mis paper. The fact given in this paper might be helpful to keep us an open mind, it is our traditional thoughts that are the largest restrictions to our minds. Thus, we must revalue all of our traditional concepts and ideas for nonlinear problems.
Shi-jun Liao
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,Shanghai 200030, China
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
996-1002
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）