ZHU Yin,LIU Xiaohua.Traveling wave solutions of the Kadomtsov - Petviashvili - Benjamin - Bona - Mahony equation[J].Journal of Yanbian University,2023,(03):250-256.
Kadomtsov - Petviashvili - Benjamin - Bona - Mahony方程的行波解
- Title:
- Traveling wave solutions of the Kadomtsov - Petviashvili - Benjamin - Bona - Mahony equation
- 文章编号:
- 1004-4353(2023)03-0250-07
- 关键词:
- KP - BBM方程; 修正辅助方程法; 行波解; 双曲函数解; 雅克比椭圆函数解
- Keywords:
- Kadomtsov - Petviashvili - Benjamin - Bona - Mahony equation; modified auxiliary equation method; traveling wave solutions; hyperbolic function solutions; Jacobi elliptic function solutions
- 分类号:
- O175.29
- 文献标志码:
- A
- 摘要:
- 利用修正的辅助方程法研究了Kadomtsov - Petviashvili - Benjamin - Bona - Mahony(KP - BBM)方程的行波解,得到了该方程的双曲余切函数解和雅克比椭圆函数解,并利用Matlab软件给出了所得解的性态行为.
- Abstract:
- The traveling wave solution of the Kadomtsov - Petviashvili - Benjamin - Bona - Mahony(KP - BBM)equation was studied by the modified auxiliary equation method.The Hyperbolic cotangent solution and the Jacobi elliptic function solution of the equation were obtained, and the sexual behavior of the obtained solution was given by using Matlab software.
参考文献/References:
[1] MANAFIAN J, ILHAN O A, ALIZADEH A.Periodic wave solutions and stability analysis for the KP - BBM equation with abundant novel interaction solutions [J].Physica Scripta, 2020,95(6):065203.
[2] WANG M, LI X, ZHANG J.The(G’/G)- expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics[J].Physics Letters A, 2008,372(4):417 - 423.
[3] AKBAR M A, ALI N H M, ZAYED E M E.Abundant exact traveling wave solutions of generalized bretherton equation via improved(G’/G)- expansion method[J].Communications in Theoretical Physics, 2012,57(2):173.
[4] AKBAR M A, HJ N, ALI M, et al.Some new exact traveling wave solutions to the(3+1)- dimensional Kadomtsev - Petviashvili equation[J].World Appl Sci J, 2012,16(11):1551 - 1558.
[5] SAHOO S, RAY S S.New travelling wave and anti - kink wave solutions of space - time fractional(3+1)- dimensional Jimbo - Miwa equation[J].Chinese Journal of Physics, 2020,67:79 - 85.
[6] ZAYED E M E, GEPREEL K A.The(G’/G)- expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics[J].Journal of Mathematical Physics, 2009,50(1):013502.
[7] AKBAR M A, ALI N H M.The alternative(G’/G)- expansion method and its applications to nonlinear partial differential equations[J].Int J Phys Sci, 2011,6(35):7910 - 7920.
[8] MOHYUD - DIN S T.The alternative(G’/G)- expansion method with generalized Riccati equation: application to fifth order(1+1)- dimensional Caudrey - Dodd - Gibbon equation[J].Int J Phys Sci, 2012,75:743.
[9] ALAM M N, LI X.Exact traveling wave solutions to higher order nonlinear equations[J].Journal of Ocean Engineering and Science, 2019,4(3):276 - 288.
[10] DEHGHAN M, MANAFIAN J.The solution of the variable coefficients fourth - order parabolic partial differential equations by the homotopy perturbation method[J].Zeitschrift für Naturforschung A, 2009,64(7/8):420 - 430.
[11] KUMAR S, KUMAR D, WAZWAZ A M.Group invariant solutions of(3+1)- dimensional generalized B - type Kadomstsev Petviashvili equation using optimal system of Lie subalgebra[J].Physica Scripta, 2019,94(6):065204.
[12] KUMAR S, KUMAR D, KHARBANDA H.Lie symmetry analysis, abundant exact solutions and dynamics of multisolitons to the(2+1)- dimensional KP - BBM equation[J].Pramana, 2021,95(1):33.
[13] MOHYUD - DIN S T, IRSHAD A, AHMED N, et al.Exact solutions of(3+1)- dimensional generalized KP equation arising in physics[J].Results in Physics, 2017,7:3901 - 3909.
[14] MANAFIAN J, MOHAMMADI I B, ABAPOUR M.Breather wave, periodic, and cross - kink solutions to the generalized Bogoyavlensky - Konopelchenko equation[J].Mathematical Methods in the Applied Sciences, 2020,43(4):1753 - 1774.
[15] SONG M, YANG C, ZHANG B.Exact solitary wave solutions of the Kadomtsov - Petviashvili - Benjamin - Bona - Mahony equation[J].Applied Mathematics and Computation, 2010,217(4):1334 - 1339.
[16] TARIQ K U H, SEADAWY A R.Soliton solutions of(3+1)- dimensional Kortewegde Vries Benjamin - Bona - Mahony, Kadomtsev - Petviashvili Benjamin - Bona - Mahony and modified Kortewegde Vries - Zakharov - Kuznetsov equations and their applications in water waves[J].Journal of King Saud University - Science, 2019,31(1):8 - 13.
[17] SAHA R S, SINGH S.New bright soliton solutions for Kadomtsev - Petviashvili - Benjamin - Bona - Mahony equations and bidirectional propagation of water wave surface[J].International Journal of Modern Physics C, 2022,33(5):2250069.
[18] MANAFIAN J, ILHAN O A, ALIZADEH A.Periodic wave solutions and stability analysis for the KP - BBM equation with abundant novel interaction solutions[J].Physica Scripta, 2020,95(6):065203.
[19] ALI A.Travelling waves solutions of the KP equation in weakly dispersive media[J].Open Physics, 2022,20(1):715 - 723.
备注/Memo
收稿日期: 2023-05-08
基金项目: 贵州省教育厅自然科学研究项目([2022]015号,QJJ2023012,QJJ2023061,QJJ2023062)
第一作者: 朱引(1998—),女,硕士研究生,研究方向为微分方程的定性分析.
通信作者: 刘小华(1975—),女,博士,教授,研究方向为微分方程的定性分析.