赵云梅;杨云杰;将艳;

• 1:红河学院数学学院
• 2:昆明学院数学系
• 3:思茅师范高等专科学校数学系

摘要(Abstract)：

利用改进的(G′/G)-展开法,求广义的(2+1)维Boussinesq方程的精确解,得到了该方程含有较多任意参数的用双曲函数、三角函数和有理函数表示的精确解,当双曲函数表示的行波解中参数取特殊值时,便得到广义的(2+1)维Boussinesq方程的孤立波解.

关键词(KeyWords)： 广义的(2+1)维Boussinesq方程;齐次平衡;改进的(G′/G)-展开法;精确解

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11161020);; 云南省科技厅项目(2011FZ193);; 昆明学院校级项目(XJ11L021)

作者(Authors): 赵云梅;杨云杰;将艳;

参考文献(References)：

• [1]Chen H T,Zhang H Q.New double periodic and multiple soliton solutions of the generalized(2+1)-dimensional Boussinesq equation[J].Chaos Solitons Fract,2004,20(4):756-769.
• [2]Song M,Shao S G.Exact solitary wave solutions of the generalized(2+1)dimensional Boussinesq equation[J].Applied Mathematics and Computation,2010,217:3557-3563.
• [3]El-Sayed S M,Kaya D.The decomposition method for solving(2+1)-dimensional Boussinesq equation and(3+1)-dimensional KP equation[J].Appl.Math.Comput,2004,157(2):523-534.
• [4]Abdel Rady A S,Osman E S,Khalfallah M.On soliton solutions of the(2+1)dimensional Boussinesqequation[J].Appl.Math.Comput.,2009,(5):28.
• [5]Chen Y,Yan Z Y,Zhang H Q.New explicit solitary wave solutions for(2+1)-dimensional Boussinesqequation and(3+1)-dimensional KP equation[J].Phys.Lett.A.,2003,307(2/3):107-113.
• [6]Liu S K,Fu Z T,Liu S D,et al.Jacobi elliptic function expansion method and periodic wave solutions ofnonlinear wave equations[J].Phys.Lett.A,2001,289(1/2):69-74.
• [7]Johnson R S.A two-dimensional Boussinesq equation for water waves and some of its solutions[J].J.FluidMech.,1996,323:65-78.
• [8]Wang M L.The(G/G)-expansion method and traveling wave solutions of nonlinear evolution equations inmathematical physics[J].Physics Letters A,2008,372(4):417-423.
• [9]Guo S M,Zhou Y B,Zhao C X.The improved(G/G)-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations[J].Applied Mathematics and Computation,2010,216:1965-1971.
• [10]Zhang S,Wang W,Tong J L.A generalized(G/G)-expansion method and its application to the(2+1)-dimensional Broer-Kaup equations[J].Applied Mathematics and Computation,2009,209:399-404.