变系数GKP方程的精确解

doi:10.6040/j.issn.1671-9352.0.2017.565

摘要/Abstract

摘要： 对一类变系数GKP方程求解,首先构造出解的形式并结合不同的辅助方程的新解及相应的Bäcklund变换,在数学计算软件的帮助下获得了该方程的无穷序列类孤子新精确解。这些解的类型包括Jacobi椭圆函数型、三角函数型、指数函数型、双曲函数型等。然后又使用假设孤立波方法研究这一类变系数GKP方程,进而得到了另类的孤立波解。

关键词: 变系数GKP方程, 辅助方程, Bä, cklund变换, 无穷序列精确解

Abstract: In order to solve a kind of GKP equation with variable coefficients, the form of the solution is first constructed then combined with the new solutions of different auxiliary equations and corresponding Bäcklund transformations. With the help of mathematical calculation software, the new exact solutions of infinite sequence soliton-like of the equation are obtained. The types of these solutions include Jacobi elliptic function type, trigonometric function type, exponential function type, hyperbolic function type, etc. Using the hypothetical solitary wave method, this kind of GKP equation with variable coefficients is studied. Then alternative solitary wave solutions are obtained.

Key words: GKP equation with variable coefficients, auxiliary equation, Bä, cklund transformation, infinite sequence exact solutions

中图分类号:

O175.2

杨飞,刘希强. 变系数GKP方程的精确解[J]. 《山东大学学报(理学版)》, 2019, 54(2): 111-120.

YANG Fei, LIU Xi-qiang. Exact solution of GKP equation with variable coefficients[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 111-120.

参考文献

[1] 许晓革,张小媛,孟祥花.Bell多项式在变系数Gardner-KP方程中的应用[J].量子电子学报,2016,33(6):671-679. XU Xiaoge, ZHANG Xiaoyuan, MENG Xianghua. The application of bell polynomials in variable coefficient Gardner-KP equation[J]. Chinese Journal of Quantum Electronics, 2016, 33(6):671-679.
[2] WAZWAZ A M. Soliton and sigular solitons for the Gardner-KP equation[J]. Applied Mathematics and Computation, 2008, 204:162-169.
[3] 严经坤.改进的F-展开法及其在一些孤立子方程中的应用[D].郑州:郑州大学,2009. YAN Jingkun. The improved F-expansion method and its application to some soliton equation[D]. Zhengzhou: Zhengzhou University, 2009.
[4] XU Bin, LIU Xiqiang. Classification,reduction,group invariant solutions and conservation laws of the Gardner-KP equation[J]. Applied Mathematics and Computation, 2009, 215:1244-1250.
[5] SHAKEEL M, MOHYUD D. Soliton solutions for the positive Gardner-KP equation by(G'/G)-expansion method[J]. Ain Shams Engineering Journal, 2014, 5:951-958.
[6] 李德生,张鸿庆.(2+1)维色散水波系统的非行波解的新族[J].中国物理,2004,13:1377-1381. LI Deshen, ZHANG Hongqing. New families of non-travelling wave solutions to the(2+1)-dimensional modified dispersive water-wave system[J]. Chinese Physics, 2004, 13:1377-1381.
[7] 马松华,方建平.扩展的(2+1)维浅水波方程的尖峰孤子解及其相互作用[J].物理学报,2012,61(18):180505:1-6. MA Songhua, FANG Jingping. Peaked soliton solutions and interaction between solitons for the extended(2+1)-dimensional shallow water wave equation[J]. Acta Physical Sinica, 2012, 61(18):180505:1-6.
[8] 套格图桑,伊丽娜.Camassa-Holm-r方程的无穷序列类孤子新解[J].物理学报,2014,3(12):1-9. Taogetusang, YI Lina. The infinite sequence class soliton solutions of the Camassa-Holm-r equation[J]. Acta Physical Sinica, 2014, 3(12):1-9.
[9] 套格图桑,斯仁道尔吉.构造变系数非线性发展方程精确解的一种方法[J].物理学报,2009,58(4):2121-2126. Taogetusang, Sirendaoerji. A method for constructing exact solutions of nonlinear evolution equations with variable coefficients[J]. Acta Physical Sinica, 2009, 58(4):2121-2126.
[10] 套格图桑,那仁满都拉.第二种椭圆方程构造变系数非线性发展方程的无穷序列精确解[J].物理学报,2011,60(9):1-12. Taogetusang, Narenmandula. The second kind of elliptic equation constructs the infinite sequence exact solution of the nonlinear evolution equation of the variable coefficient[J]. Acta Physical Sinica, 2011, 60(9):1-12.
[11] 白玉梅,套格图桑.变系数(2+1)维Broer-Kaup方程的无穷序列新精确解[J].内蒙古师范大学学报(自然科学版),2015,44(6):743-748. BAI Yumei, Taogetusang. New exact solutions in infinite sequence of variable coefficient(2+1)-dimensional Broer-Kaup equation[J]. Journal of Inner Mongolia Normal University(Natural Science Edition), 2015, 44(6):743-748.
[12] 套格图桑,斯仁道尔吉,李姝敏. Riccati方程的新应用[J].中国物理B,2010,19(8):080303:1-8. Taogetusang, Sirendaoerji, LI Shumin. New application to Riccati equation[J]. Chinese Physics B, 2010, 19(8):080303:1-8.
[13] 王岗伟,刘希强,张颖元.变系数mKdV方程的精确解[J].井冈山大学学报(自然科学版),2012,33(5):1-5. WANG Gangwei, LIU Xiqiang, ZHANG Yiyuan. Exact solutions of mKdV equations with variable coefficients[J]. Journal of Jinggangshan University(Natural Science), 2012, 33(5):1-5.
[14] 孙玉真,王振立,王岗伟,等.广义变系数五阶KdV和BBM方程的孤立波解[J].量子电子学报,2013,30(4):398-404. SUN Yuzhen, WANG Zhenli, WANG Gangwei, et al. Soliton solutions for generalized fifth-order KdV and BBM equations with variable coefficients[J]. Chinese Journal of Quantum Electronics, 2013, 30(4):398-404.
[15] 洪宝剑,卢殿臣.变系数(2+1)维Broer-Kaup方程新的类孤子解[J].原子与分子物理学报,2008,25(1):130-134. HONG Baojian, LU Dianchen. New soliton-like solutions of the variable coefficient(2+1)-dimensional Broer-Kaup equation[J]. Atomic and Molecular Physics, 2008, 25(1):130-134.
[16] WAZWAZ A M, TRIKI H. Soliton solutions for a generalized KdV and BBM equations with-time-dependent coefficients[J]. Communications in Nonlinear Science & Numerical Simulation, 2011, 16:1122-1126.

相关文章 15

[1]	冯孝周,徐敏,王国珲. 具有B-D反应项与毒素影响的捕食系统的共存解[J]. 《山东大学学报(理学版)》, 2018, 53(12): 53-61.
[2]	马霞,姚美萍. 汉坦病毒传播模型行波解的存在性[J]. 《山东大学学报(理学版)》, 2018, 53(12): 48-52.
[3]	甄苇苇,曾剑,任建龙. 基于变分理论与时间相关的抛物型反源问题[J]. 山东大学学报（理学版）, 2018, 53(10): 61-71.
[4]	李会会,刘希强,辛祥鹏. 变系数Benjamin-Bona-Mahony-Burgers方程的微分不变量和精确解[J]. 山东大学学报（理学版）, 2018, 53(10): 51-60.
[5]	杜广伟. 具有次临界增长的椭圆障碍问题解的正则性[J]. 山东大学学报（理学版）, 2018, 53(6): 57-63.
[6]	董亚莹. 一类空间退化的捕食-食饵模型的全局分歧结构[J]. 山东大学学报（理学版）, 2018, 53(4): 76-84.
[7]	张道祥,孙光讯,马媛,陈金琼,周文. 带有Holling-III功能反应和线性收获效应的时滞扩散捕食者-食饵系统Hopf分支和空间斑图[J]. 山东大学学报（理学版）, 2018, 53(4): 85-94.
[8]	张泰年,李照兴. 一类退化抛物型方程反问题的收敛性分析[J]. 山东大学学报（理学版）, 2017, 52(8): 35-42.
[9]	董莉. 两类非线性波动方程解的爆破时间的下确界[J]. 山东大学学报（理学版）, 2017, 52(4): 56-60.
[10]	段双双,钱媛媛. Keller-Segel型交叉扩散方程组柯西问题解的逐点估计[J]. 山东大学学报（理学版）, 2017, 52(4): 40-47.
[11]	李玉,刘希强. 扩展的KP-Benjamin-Bona-Mahoney方程的对称、约化和精确解[J]. 山东大学学报（理学版）, 2017, 52(2): 77-84.
[12]	张道祥, 赵李鲜, 胡伟. 一类三种群食物链模型中交错扩散引起的Turing不稳定[J]. 山东大学学报（理学版）, 2017, 52(1): 88-97.
[13]	付娟,张睿,王彩军,张婧. 具有Beddington-DeAngelis功能反应项的捕食-食饵扩散模型的稳定性[J]. 山东大学学报（理学版）, 2016, 51(11): 115-122.
[14]	宋萌萌,尚海锋. 具测度初值的非线性抛物方程组的Cauchy问题[J]. 山东大学学报（理学版）, 2016, 51(10): 41-47.
[15]	李月霞,张丽娜,张晓杰. 2维Lengyel-Epstein模型的分支结构[J]. 山东大学学报（理学版）, 2016, 51(8): 74-78.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed