(2+1)维extended Kadomtsev-Petviashvili方程的混合型精确解
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摘要
Kadomtsev-Petviashvili方程的类型非常多,描述很多数学物理现象,研究Kadomtsev-Petviashvili方程的精确解是非常有必要的。本文主要讨论(2+1)维extended Kadomtsev-Petviashvili方程。基于Hirota双线性形式和符号计算软件Mathematica,考虑指数函数,三角函数和双曲函数的混合,我们获得了(2+1)维extended Kadomtsev-Petviashvili方程一些新的混合型精确解,并利用一些三维图形展示了这些解的物理结构和特点。
The Kadomtsev-Petviashvili equations are rich in typeand theydescribe many mathematicaland physical phenomena.It is necessary to study the exact solution of the Kadomtsev-Petviashvili equation.In this paper,we mainly discuss the(2+1) dimensional extended Kadomtsev-Petviashvili equation.Based on the Hirota bilinear form andthe symbolic computing software Mathematica,andconsidering the mixing of exponential functions,trigonometric functions and hyperbolic functions,we obtain some new mixed exact solutions of the(2+1) dimension extended Kadomtsev-Petviashvili equation.The physical structure and characteristics of these solutionsare illustrated by using some three-dimensional graphics.
The Kadomtsev-Petviashvili equations are rich in typeand theydescribe many mathematicaland physical phenomena.It is necessary to study the exact solution of the Kadomtsev-Petviashvili equation.In this paper,we mainly discuss the(2+1) dimensional extended Kadomtsev-Petviashvili equation.Based on the Hirota bilinear form andthe symbolic computing software Mathematica,andconsidering the mixing of exponential functions,trigonometric functions and hyperbolic functions,we obtain some new mixed exact solutions of the(2+1) dimension extended Kadomtsev-Petviashvili equation.The physical structure and characteristics of these solutionsare illustrated by using some three-dimensional graphics.
引文
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[2] 熊伟.(3+1)维Yu-Toda-Sasa-Fukuyama方程新的周期孤波解[J].南昌大学学报(理科版),2017,41(3):211-215.
[3] 温丹华,郑道都.一个新型的带自相容源的变系数(3+1)维KP方程[J].郑州大学学报(理学版),2016,48(1):37-40.
[4] 李向正,王乔丹,张金良.变系数KP方程和变系数广义KP方程的变速孤波解[J].河南科技大学学报(自然科学版),2016,37(6):82-84.
[5] 付中华,李良树.(G'/G)展开法求解(3+1)维Jimbo-Miwa方程新的精确解[J].南昌大学学报(理科版),2017,41(5):418-422.
[6] 程丽.推广KP方程的非奇异有理解[J].温州大学学报(自然科学版),2017,38(3):1-7.
[7] 吴娇.Wick型随机偏微分KP方程的精确解[J].兰州文理学院学报(自然科学版),2016,30(5):5-11.
[8] 李婷,沃维丰.GdKP方程的最优系统和群不变解[J].纯粹数学与应用数学,2016,32(3):324-330.
[9] LIU J G,DU J Q,ZENG Z F,NIE B.New three-wave solutions for the(3+1)-dimensional boiti-leon-manna-pempinelli equation[J].Nonlinear Dynamics,2017,88(1):655-661.
[10] 傅海明,戴正德.(2+1)维广义KdV方程的周期孤波解[J].平顶山学院学报,2013,28(5):35-38.
[11] 刘建国,曾志芳.变系数Sine-Gordon方程的B?cklund变换和新的精确解[J].系统科学与数学,2014,34(6):763-768.
[12] 袁娜.(3+1)维Boiti-Leon-Manna-Pempinelli方程新的三波解[J].南昌大学学报(理科版),2017,41(4):319-323.
[13] 秦立春.Caudrey-Dodd-Gibbon-Kaeada方程的新双周期孤子解[J].南昌大学学报(理科版),2017,41(6):524-530.
[14] LI Y Z,LIU J G.New periodic solitary wave solutions for the new (2+1)-dimensional Korteweg-de Vries equation[J].Nonlinear Dyn,2018,91(1):497-504.
[15] LIU J G,TIAN Y,HU J G.New non-traveling wave solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation[J].Appl.Math.Lett,2018,79:162-168.
[16] WAZWAZ A M,EL-TANTAWY S A.Solving the (3+1)-dimensional KP-boussinesq and BKP-boussinesq equations by the simplified hirota's method[J].Nonlinear Dyn,2017,88(4):3017-3021.
[17] SOLOMON M,ZHOU Y,MA W X.Lump solutions to a (2+1)-dimensional extended KP equation,Comput.Math.Appl,2018,75(7):2414-2419.