广义Riccati方程统一的带多参量的有理指数函数解
A Uniform Rational-Exponent Function Solution with Multi-Parameters for the Generalized Riccati Equation
DOI: 10.12677/AAM.2021.1012476, PDF,    科研立项经费支持
作者: 留 庆：丽水学院工学院，浙江 丽水；浙江嘉利(丽水)工业股份有限公司，浙江 丽水；漆爱冬, 陈 伟, 周小伟：浙江嘉利(丽水)工业股份有限公司，浙江 丽水
关键词: Riccati方程；有理指数函数解；双曲函数解；三角函数解；q变形函数解；Riccati Equation； Rational-Exponent Function Solution； Hyperbolic Function Solution； Trigonometric Function Solution； q-Deformation Function Solution
摘要: 一个广义Riccati方程的带有多参数的万能有理指数函数解被获得，这个解不仅包含Riccati方程已知的各种类型的双曲函数解、三角函数解和q变形函数解，而且还包含大量有理指数函数解。我们用一个统一的有理指数函数解将Riccati方程所有类型的解统一起来。
Abstract: We derive a universal rational-exponent function solution with multi parameters, which contains not only well-known hyperbolic function solutions, trigonometric function solutions and q-deformation function solutions, but also new rational-exponent function solutions for the generalized Riccati equation. Based on this uniform rational-exponent solution, we unite all kinds of solutions for Riccati equation.
文章引用：留庆, 漆爱冬, 陈伟, 周小伟. 广义Riccati方程统一的带多参量的有理指数函数解[J]. 应用数学进展, 2021, 10(12): 4477-4482. https://doi.org/10.12677/AAM.2021.1012476

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