Abstract
In this paper we give some results of integrability and several classes of integrable equations of first-order nonlinear ordinary differential equations. Many known results of integrability and integrable equations are special cases of them. They may be applied in physics and mechanics, and to derive soliton equations and find soliton solutions.
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References
Li Hong-xiang, Elementary quadratures of ordinary differential equations,Amer. Math. Monthly,89, 3 (1982), 198–208;MR 83d: 34008.
Wang Cun-zheng, Formulas for solutions of differential equations, I. Formulas for solutions of higher-order linear and nonlinear ordinary differential equations with variable coefficients,Acta Math. Appl. Sinica,5, 3 (1982), 274–284;MR 84c: 34003. (in Chinese)
Li Hong-xiang, On periodic solutions of several classes of R Riccati's equation and second-order differential equations,Appl. Math. and Mech. (English Edition),3, 2 (1982), 225–232;MR 83m: 34036.
Li Hong-xiang, On the finding of solutions for several classes of higher-order linear differential equations with variable coefficients,Acta Math. Appl. Sinica,6, 1 (1983), 29–33:MR 85h: 34003. (in Chinese)
Wang Cun-zheng, Formulas for solutions of differential equations,Kexue Tongbao,30, 16 (1985), 1211–1214. (Chinese Ed.)
Wang Cun-zheng, Several nonlinear partial differential equations and their soliton solutions,Acta Mathematica Scientia,5, 1 (1985), 43–51. (in Chinese)
Kamke, E., Differentialgleichungen: Lösungsmethoden und Lösungen, I.Gewöhnliche Differentialgleichungen, 9 Aufl., B. G. Teubner Stuttgart (1977).
Murphy, G. M.,Ordinary Differential Equations and Their Solutions, D. Van Nostrand, New York (1960).
Zheng Long-xi, On several types of integrable first-order differential equations with variable coefficients,Higher Math.,2, 4 (1986), 158–162. (in Chinese)
Li Hong-xiang, Some supplements to Kamke's handbook “Gewöhnliche Differentialgleichungen”, I, II,J. Shanghai Inst. of Railway Tech.,7, 1 (1986), 9–22;7, 2 (1986), 27–38. (in Chinese).
Li Hong-xiang and Fan Xing, Re-discussion on elementary quadratures of ordinary differential equatins,J. Shanghai Inst. of Railway Tech.,8, 2 (1987), 1–15.
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Communicated by Lou Shi-bo
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Hong-xiang, L., Starc, Z.F. Several classes of integrable nonlinear ordinary differential equations (I) first-order equations. Appl Math Mech 11, 263–269 (1990). https://doi.org/10.1007/BF02015207
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DOI: https://doi.org/10.1007/BF02015207