文章基本信息

标题：A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application
本地全文：下载
作者：Xiao-Feng Yang ; Zi-Chen Deng ; Yi Wei 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2015
卷号：2015
期号：1
页码：117
DOI：10.1186/s13662-015-0452-4
语种：English
出版社：Hindawi Publishing Corporation
摘要：The Riccati-Bernoulli sub-ODE method is firstly proposed to construct exact traveling wave solutions, solitary wave solutions, and peaked wave solutions for nonlinear partial differential equations. A Bäcklund transformation of the Riccati-Bernoulli equation is given. By using a traveling wave transformation and the Riccati-Bernoulli equation, nonlinear partial differential equations can be converted into a set of algebraic equations. Exact solutions of nonlinear partial differential equations can be obtained by solving a set of algebraic equations. By applying the Riccati-Bernoulli sub-ODE method to the Eckhaus equation, the nonlinear fractional Klein-Gordon equation, the generalized Ostrovsky equation, and the generalized Zakharov-Kuznetsov-Burgers equation, traveling solutions, solitary wave solutions, and peaked wave solutions are obtained directly. Applying a Bäcklund transformation of the Riccati-Bernoulli equation, an infinite sequence of solutions of the above equations is obtained. The proposed method provides a powerful and simple mathematical tool for solving some nonlinear partial differential equations in mathematical physics.
关键词：Riccati-Bernoulli sub-ODE method ; Bäcklund transformation ; traveling wave solution ; solitary wave solution ; peaked wave solution