ZHANG Hong-qing, YAN Zhen-ya. Two Types of New Algorithms for Finding Explicit Analytical Solutions of Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1285-1292.
 Citation: ZHANG Hong-qing, YAN Zhen-ya. Two Types of New Algorithms for Finding Explicit Analytical Solutions of Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1285-1292.

# Two Types of New Algorithms for Finding Explicit Analytical Solutions of Nonlinear Differential Equations

• Received Date: 2000-01-14
• Rev Recd Date: 2000-08-21
• Publish Date: 2000-12-15
• The idea of AC=BD was applied to solve the nonlinear differential equations.Suppose that Au=0 is a given equation to be solved and Dv=0 is an equation to be easily solved.If the transformation u=Cv is obtained so that v satisfies Dv=0,then the solutions for Au=0 can be found.In order to illustrate this approach,several examples about the transformation C are given.
•  [1] Ablowitz M J, Clarkson P A. Soliton Nonlinear Evolution Equations and Inverse Scatting[M]. New York: Cambridge University Press,1991. [2] Olver P J. Applications of Lie Groups to Differential Equatons[M]. New York: Springer-Verlag,1986. [3] Bluman G W, Kumei S. Symmetries and Differential Equations[M]. New York: Springer-Verlag,1989. [4] Gu C H, Li Y S,Guo B L, et al. Soliton Theory and Its Ap plication[M]. Berlin: Springer,1995. [5] Cox D. Ideal Varieties and Algorithms[M]. New York: Springer-Verlag,1991. [6] ZHANG Hong-qing. The algebraization, mechanization, symple ctication and geometrization for mechanics[A]. In: LIU Yu-lu Ed. Modern Math Mech(MMM-Ⅶ)[C]. Shanghai: Shanghai University Press,1997,20. [7] ZHANG Hong-qing. A united theory on general solution of systems of elasticity[J]. J Dalian University of Technology,1978,18 (1):25-47. [8] ZHANG Hong-qing. Algebraic constructure for general solutions of linear operator systems[J]. Acta Mechanica Sinica,1981,13(special issure):26-31. [9] 张鸿庆. Mexwell方程的多余阶次与恰当解[J]. 应用数学和力学,1981,2(3):321-331. [10] ZHANG Hong-qing, WANG Zhen-yu. The completeness and appro ximation of Hu Haichang's solution[J]. Kexue Tongbao,1986,31(10): 667-672. [11] ZHANG Hong-qing, WU Fang-xiang. General solutions for a class of system of partial differential equations and its application in the theory of shells[J]. Acta Mechanica Sinica,1992,24(5):700-705. [12] 张鸿庆,杨光. 变系数偏微分方程组一般解的构造[J]. 应用数 学和力学,1991,12(2):135-139. [13] ZHANG Hong-qing, YAN Zhen-ya. New explicit and exact solutions for nonlinear evolution equations[J]. Math Appl,1999,12(1): 76-81. [14] YAN Zhen-ya, ZHANG Hong-qing. New explicit and exact solutions for a system of variant Boussinesq equations in mathematical physics[J]. Phys Lett A,1999,252(2):291-297. [15] YAN Zhen-ya, ZHANG Hong-qing, FAN En-gui. New explicit travelling wave solutions for a class of nonlinear evolution equation[J]. Acta Phys Sin,1999,48(1):1-5. [16] YAN Zhen-ya, ZHANG Hong-qing. Explicit and exact solutions for the generalized reaction duffing equation[J]. Commun Nonl Sci Numer Simu,1999,4(3):224-229. [17] YAN Zhen-ya, ZHANG Hong-qing. Backlund transformation and exact solutions for (2+1)-dimensional KPP equation[J]. Commun Nonl Sci Numer Simu,1999,4(2):146-151. [18] Wu W. On the zeros of polynomial set[J]. Kexue Tongbao,1986,31(1):1-5. [19] Wu W. On the foundation of algebraic differential geometry[J]. MMR-Preptints,1989,3(1):1-6.

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