基于扩展G′/G-展开法的两个非线性拟抛物型方程的精确解  

The Exact Solutions of Two Nonlinear Pseudoparabolic Equations Based on Extended(G′/G)-Expansion Method

作　　者：范凯[1] 刘斌[1] 宋叔尼[2] 范圆圆 FAN Kai;LIU Bin;SONG Shu-ni;FAN Yuan-yuan(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China;School of Sciences,Northeastern University,Shenyang 110819,China)

机构地区：[1]太原科技大学应用科学学院,山西太原030024 [2]东北大学理学院,辽宁沈阳110819

出　　处：《中北大学学报（自然科学版）》2018年第6期648-653,共6页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11701406);辽宁省自然科学基金资助项目(201602259)

摘　　要：对两个重要的非线性拟抛物物理模型,Benjamin-Bona-Mahony-Peregrine-Burgers(BBMPB)和Oskolkov-Benjamin-Bona-Mahony-Burgers(OBBMB)方程进行了研究.使用扩展的G′/G-函数展开法,借助符号计算软件Maple,获得了它们新的精确行波解,并验证了它们的正确性.这些解包括双曲函数精解,三角周期解和有理函数解.精确解的获得,有助于解释以这两个方程为模型的一些实际物理现象、为数值解的进一步研究提供一定的参考.获得的结果证实该方法也可以用于求解一些其他的非线性拟抛物模型方程.Two important nonlinear pseudoparabolic physical models,the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB)equation,and the Oskolkov-Benjamin-Bona-Mahony-Burgers (OBBMB)equation were studied.The extended (G′/G)-expansion method and symbolic computation software Maple were used to obtain the new exact traveling wave solutions of these equations,and verified the correctness.These solutions include function fine solutions,triangular periodic solutions and rational function solutions.These exact solutions can help to explain some practical physical phenomena which are modelled on these equations,and provide a certain reference for the further study of the numerical solution. The obtained results confirm that the proposed methods can also be used to solve some of the other nonlinear pseudoparabolic model equations.

关 键 词：扩展的G′/G-函数展开法:BBMPB方程 OBBMB方程 扭结解 非线性拟抛物方程 

分 类 号：O175.29[理学—数学]