Logistic函数作为多个非线性微分方程的解
Logistic function as solution of many nonlinear differential equations
摘要：
证明了逻辑函数是Riccati方程、某些二阶非线性常微分方程和许多三阶非线性常微分方程的解。给出了具有逻辑函数形式解的微分方程列表。介绍了求非线性偏微分方程精确解的简单方法。该方法的本质是基于比较的非线性微分方程从偏微分方程与标准的微分方程具有解决方案的形式的逻辑函数。证明了逻辑函数在求解非线性微分方程精确解中的广泛应用。
英文摘要：
The logistic function is shown to be solution of the Riccati equation, some second-order nonlinear ordinary differential equations and many third-order nonlinear ordinary differential equations. The list of the differential equations having solution in the form of the logistic function is presented. The simple method of finding exact solutions of nonlinear partial differential equations (PDEs) is introduced. The essence of the method is based on comparison of nonlinear differential equations obtained from PDEs with standard differential equations having solution in the form of the logistic function. The wide application of the logistic function for finding exact solutions of nonlinear differential equations is demonstrated.
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