期刊
APPLIED MATHEMATICAL MODELLING
卷 39, 期 18, 页码 5733-5742出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.01.048
关键词
Logistic function; Nonlinear differential equation; Partial differential equation; Exact solution; Solitary wave solution
资金
- Russian Science Foundation [14-11-00258]
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. (C) 2015 Elsevier Inc. All rights reserved.
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