数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1064-1076.
(3+1)维广义Kadomtsev-Petviashvili方程新的精确周期孤立波解
李颖1,*(
),刘建国2,阳连武1
- 1 宜春学院数学与计算机科学学院 江西宜春 336000
2 江西中医药大学计算机学院 南昌 330004
-
收稿日期:2018-08-30出版日期:2019-10-26发布日期:2019-11-08 -
通讯作者:李颖 E-mail:jxsdsxx@bupt.edu.cn -
基金资助:国家自然科学基金(61377067);江西省教育厅科技项目(GJJ170889)
New Exact Periodic Solitary Wave Solutions for the (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation
Ying Li1,*(),Jianguo Liu2,Lianwu Yang1
- 1 School of Mathematical and Computer Science, Yichun University, Jiangxi Yichun 336000
2 College of Computer, Jiangxi University of Traditional Chinese Medicine, Nanchang 330004
-
Received:2018-08-30Online:2019-10-26Published:2019-11-08 -
Contact:Ying Li E-mail:jxsdsxx@bupt.edu.cn -
Supported by:the NSFC(61377067);the Jiangxi Provincial Department of Education(GJJ170889)
摘要：
该文研究了广义Kadomtsev-Petviashvili方程，该方程是依赖于横坐标的小振幅慢波非线性长波演化方程.利用Hirota的双线性形式与扩展同宿测试方法，（3+1）维广义Kadomtsev-Petviashvili方程新的精确周期孤立波解被获得，这些获得的结果和已知文献中的结论都不同.在符号计算的帮助下，这些新的周期波精确解的性质和特点通过一些图形进行了展示.
中图分类号:
- O175.2
引用本文
李颖,刘建国,阳连武. (3+1)维广义Kadomtsev-Petviashvili方程新的精确周期孤立波解[J]. 数学物理学报, 2019, 39(5): 1064-1076.
Ying Li,Jianguo Liu,Lianwu Yang. New Exact Periodic Solitary Wave Solutions for the (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation[J]. Acta mathematica scientia,Series A, 2019, 39(5): 1064-1076.
图 1
$k_3 = -2$, ${\cal J}_3 = -5$, $x = 2$, ${\cal I}_1 = {\cal I}_2 = {\cal I}_3 = {\cal J}_1 = {\cal J}_2 = {\cal K}_2 = {\cal K}_3 = 1$, $\epsilon_1 = 1$, (a) $z = -5$, (b) $z = 0$, (c) $z = 5$"
图 1
图 2
$k_2 = -2$, $\epsilon_2 = -1$, $t = 5$, $\epsilon_3 = -1$, $k_3 = {\cal J}_1 = 2$, ${\cal I}_1 = {\cal I}_2 = {\cal I}_3 = {\cal K}_3 = 1$, $\epsilon_1 = 1$, (a) $z = -5$, (b) $z = 0$, (c) $z = 5$"
图 2
图 3
$\epsilon_4 = \epsilon_5 = 1$, $k_3 = -2$, ${\cal I}_1 = {\cal I}_2 = {\cal K}_1 = k_2 = {\cal J}_1 = {\cal J}_2 = {\cal J}_3 = {\cal K}_3 = 1$, $z = 2$, (a) $t = -2$, (b) $t = 0$, (c) $t = 2$"
图 3
图 4
${\cal I}_1 = {\cal K}_2 = z = 2$, ${\cal I}_3 = -1$, ${\cal I}_2 = 3$, $k_1 = {\cal J}_1 = {\cal K}_1 = 1$, $k_3 = -2$, ${\cal J}_2 = 4$, ${\cal L}_2 = 5$, $\epsilon _6 = 1$, (a) $t = -2$, (b) $t = 0$, (c) $t = 2$"
图 4
图 5
$k_3 = -2$, $\epsilon _9 = \epsilon _{10} = 1$, $x = 0.2$, ${\cal I}_2 = k_1 = k_2 = {\cal J}_1 = {\cal K}_1 = 1$, ${\cal J}_3 = 2$, (a) $t = -1$, (b) $t = 0$, (c) $t = 1$"
图 5
图 6
$k_3 = -2$, $\epsilon _{13} = 1$, $z = 2$, ${\cal I}_2 = k_1 = k_2 = {\cal J}_1 = {\cal K}_1 = 1$, ${\cal J}_3 = 2$, (a) $y = -5$, (b) $y = 0$, (c) $y = 5$"
图 6
图 7
$k_3 = -2$, $\epsilon _{14} = \epsilon _{15} = 1$, $x = -5$, ${\cal I}_1 = k_1 = k_2 = {\cal J}_1 = {\cal K}_1 = 1$, ${\cal J}_3 = 2$, (a) $z = -5$, (b) $z = 0$, (c) $z = 5$"
图 7
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