数学物理学报 ›› 2018, Vol. 38 ›› Issue (6): 1193-1204.
收稿日期:
2017-10-23
出版日期:
2018-12-26
发布日期:
2018-12-27
通讯作者:
危寰
E-mail:395625298@qq.com
基金资助:
Huan Wei1,*(),Lianwu Yang1,Jianguo Liu2
Received:
2017-10-23
Online:
2018-12-26
Published:
2018-12-27
Contact:
Huan Wei
E-mail:395625298@qq.com
Supported by:
摘要:
该文利用Hirota双线性形式和广义三波测试法构建了(3+1)维Potential-Yu-Toda-Sasa-Fukuyama方程新的多周期孤子解.其中有一些完全新的周期孤子解,包括周期性交叉扭结波解、周期性双孤立波解和呼吸型双孤立波解.借助于符号计算,呼吸子和孤子的相互作用及传播特点被一些图形展示出来.
中图分类号:
危寰,阳连武,刘建国. (3+1)维Potential-Yu-Toda-Sasa-Fukuyama方程新的多周期孤子解[J]. 数学物理学报, 2018, 38(6): 1193-1204.
Huan Wei,Lianwu Yang,Jianguo Liu. New Multiple Periodic-Soliton Solutions for the -Dimensional Potential-YTSF Equation[J]. Acta mathematica scientia,Series A, 2018, 38(6): 1193-1204.
1 | Lü X , Ma W X , Yu J , Khalique C M . Solitary waves with the madelung fluid description:a generalized derivative nonlinear schrödinger equation. Commun Nonlinear Sci, 2016, 31 (1/3): 40- 46 |
2 |
陈传军, 张晓艳, 赵鑫. 一维非线性抛物问题两层网格有限体积元逼近. 数学物理学报, 2017, 37A (5): 962- 975
doi: 10.3969/j.issn.1003-3998.2017.05.015 |
Chen C J , Zhang X Y , Zhao X . A two-grid finite volume element approximation for one-dimensional nonlinear parabolic equations. Acta Math Sci, 2017, 37A (5): 962- 975
doi: 10.3969/j.issn.1003-3998.2017.05.015 |
|
3 |
Ma W X , Meng J H , Zhang M S . Nonlinear bi-integrable couplings with Hamiltonian structures. Math Comput Simulat, 2016, 127: 166- 177
doi: 10.1016/j.matcom.2013.11.007 |
4 |
Liu J G , He Y . Abundant lump and lump-kink solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation. Nonlinear Dyn, 2018
doi: 10.1007/s11071-018-4111-7 |
5 | 魏含玉, 夏铁成. 广义Broer-Kaup-Kupershmidt孤子方程的拟周期解. 数学物理学报, 2016, 36A (2): 317- 327 |
Wei H Y , Xia T C . Quasi-periodic solution of the generalized Broer-Kaup-Kupershmidt soliton equation. Acta Math Sci, 2016, 36A (2): 317- 327 | |
6 |
虞静, 韩敬伟, 王立洪, 贺劲松. 散焦mKdV方程的N重暗孤子解的行列式表示. 数学物理学报, 2016, 36A (1): 14- 26
doi: 10.3969/j.issn.1003-3998.2016.01.002 |
Yu J , Han J W , Wang L H , He J S . Determinant representation of dark N-soliton solution for the defocusing modified Korteweg-de Vries (mKdV) equation. Acta Math Sci, 2016, 36A (1): 14- 26
doi: 10.3969/j.issn.1003-3998.2016.01.002 |
|
7 |
Zhang J B , Ma W X . Mixed lump-kink solutions to the bkp equation. Comput Math Appl, 2017, 74: 591- 596
doi: 10.1016/j.camwa.2017.05.010 |
8 |
Ma W X , Zhou Y . Reduced D-Kaup-Newell soliton hierarchies from sl(2, R) and so(3, R). Int J Geom Methods M, 2016, 13: 1650105
doi: 10.1142/S021988781650105X |
9 | 陈林. 一类拟线性Kirchhoff型椭圆方程组多解的存在性. 数学物理学报, 2017, 37A (4): 671- 683 |
Chen L . Multiple solutions for a quasilinear elliptic system of Kirchhoff type. Acta Math Sci, 2017, 37A (4): 674- 683 | |
10 |
Liu J G , Zhou L , He Y . Multiple soliton solutions for the new (2+1)-dimensional Korteweg-de Vries equation by multiple exp-function method. Appl Math Lett, 2018, 80: 71- 78
doi: 10.1016/j.aml.2018.01.010 |
11 |
廖家锋, 李红英. 带Sobolev临界指数的超线性Kirchhoff型方程正解的存在性与多解性. 数学物理学报, 2017, 37A (6): 1119- 1124
doi: 10.3969/j.issn.1003-3998.2017.06.011 |
Liao J F , Li H Y . Existence and multiplicity of positive solutions for the superlinear Kirchhoff-type equations with critical Sobolev exponent. Acta Math Sci, 2017, 37A (6): 1119- 1124
doi: 10.3969/j.issn.1003-3998.2017.06.011 |
|
12 |
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. Nonlinear Dyn, 2017, 88 (1): 655- 661
doi: 10.1007/s11071-016-3267-2 |
13 |
Ma W X , Yong X , Zhang H Q . Diversity of interaction solutions to the (2+1)-dimensional Ito equation. Comput Math Appl, 2017
doi: 10.1016/j.camwa.2017.09.013 |
14 |
Liu J G , He Y . New periodic solitary wave solutions for the (3+1)-dimensional generalized shallow water equation. Nonlinear Dyn, 2017, 90 (1): 363- 369
doi: 10.1007/s11071-017-3667-y |
15 |
邵光明, 柴晓娟. Navier-Stokes-Fourier方程的可压逼近. 数学物理学报, 2017, 37A (6): 1070- 1084
doi: 10.3969/j.issn.1003-3998.2017.06.007 |
Shao G M , Chai X J . Approximation of the incompressible Navier-Stokes-Fourier system by the artificial compressibility method. Acta Math Sci, 2017, 37A (6): 1070- 1084
doi: 10.3969/j.issn.1003-3998.2017.06.007 |
|
16 |
Yang J Y , Ma W X , Qin Z . Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation. Anal Math Phys, 2017
doi: 10.1007/s13324-017-0181-9 |
17 |
李琴, 杨作东. 含变号位势的p-Kirchhoff型方程组无穷多个高能量解的存在性. 数学物理学报, 2017, 37A (5): 869- 876
doi: 10.3969/j.issn.1003-3998.2017.05.008 |
Li Q , Yang Z D . Infinitely many high energy solutions of p-Kirchhoff-type system with sign-changing weight. Acta Math Sci, 2017, 37A (5): 869- 876
doi: 10.3969/j.issn.1003-3998.2017.05.008 |
|
18 |
Liu J G , Tian Y , Hu J G . New non-traveling wave solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Appl Math Lett, 2018, 79: 162- 168
doi: 10.1016/j.aml.2017.12.011 |
19 |
Zhao H Q , Ma W X . Mixed lump-kink solutions to the KP equation. Comput Math Appl, 2017, 74: 1399- 1405
doi: 10.1016/j.camwa.2017.06.034 |
20 | Ablowitz M J , Clarkson P A . Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform. London: Cambridge University Press, 1990 |
21 |
Liu J G , Li Y Z , Wei G M . Auto-Bäcklund transformation and soliton-typed solutions of the generalized Variable-Coefficient KP equation. Chin Phys Lett, 2006, 23 (7): 1670- 1673
doi: 10.1088/0256-307X/23/7/004 |
22 |
Wazwaz A M . Multiple soliton solutions and multiple singular soliton solutions for (2+1)-dimensional shallow water wave equations. Phys Lett A, 2009, 373: 2927- 2930
doi: 10.1016/j.physleta.2009.06.026 |
23 | Xie T C , Li B , Zhang H Q . New explicit and exact solutions for the Nizhnik-Novikov-Vesselov equation. Appl Math E-Notes, 2001, 1: 139- 142 |
24 |
Fan E , Zhang H . Anote on the homogeneous balance method. Phys Lett A, 1998, 246: 403- 406
doi: 10.1016/S0375-9601(98)00547-7 |
25 |
Zhang S . The periodic wave solutions for the (2+1) dimensional Konopelchenko-Dubrovsky equations. Chaos Soliton Fract, 2006, 30: 1213- 1220
doi: 10.1016/j.chaos.2005.08.201 |
26 |
El-Sabbagh M F , Ali A T . Nonclassical symmetries for nonlinear partial differential equations via compatibility. Commun Theor Phys, 2011, 56: 611- 616
doi: 10.1088/0253-6102/56/4/02 |
27 |
Dai C Q , Wang Y Y , Zhang J F . Analytical spatiotemporal localizations for the generalized (3+1)-dimensional nonlinear Schrödinger equation. Opt Lett, 2010, 35: 1437- 1439
doi: 10.1364/OL.35.001437 |
28 |
Zhang S . A generalized auxiliary equation method and its application to (2+1)-dimensional Korteweg-de Vries equations. Comput Math Appl, 2007, 54: 1028- 1038
doi: 10.1016/j.camwa.2006.12.046 |
29 |
Wang C J , Dai Z D , Mu G , Lin S Q . New exact periodic solitary-wave solutions for new (2+1)-dimensional KdV equation. Commun Theor Phys, 2009, 52: 862- 864
doi: 10.1088/0253-6102/52/5/21 |
30 | Dai Z D , Lin S Q , Fu H M , Zeng X P . Exact three-wave solutions for the KP equation. Appl Math Comput, 2010, 216 (5): 1599- 1604 |
31 |
Yu S J , Toda K , Sasa N , Fukuyama T . N-soliton solutions to the Bogoyavlenskii-Schiff equation and a quest for the soliton solution in (3+1) dimensions. J Phys A:Math Gen, 1998, 31: 3337- 3347
doi: 10.1088/0305-4470/31/14/018 |
32 |
Bruzón M S , Gandarias M L , Muriel S , Ramíres K H , Saez S , Romero F R . The Calogero-Bogoyavlenskii-Schiff equation in dimension 2+1. Teoret Mat Fiz, 2003, 137: 14- 26
doi: 10.4213/tmf |
33 | Calogero F , Degasperis A . Nonlinear evolution equations solvable by the inverse spectral transform I. Nuovo Cimento B, 1976, 32: 201- 242 |
34 |
Yan Z Y . New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation. Phys Lett A, 2003, 318: 78- 83
doi: 10.1016/j.physleta.2003.08.073 |
35 |
Bai C L , Zhao H . Generalized extended tanh-function method and its application. Chaos Soliton Fract, 2006, 27: 1026- 1035
doi: 10.1016/j.chaos.2005.04.069 |
36 |
Zhang T X , Xuan H N , Zhang D F , Wang C J . Non-travelling wave solutions to a (3+1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures. Chaos Soliton Fract, 2007, 34: 1006- 1013
doi: 10.1016/j.chaos.2006.04.005 |
37 | Song L N , Zhang H Q . A new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the (3+1)-dimensional potential-YTSF equation. Appl Math Comput, 2007, 189: 560- 566 |
38 |
Liu J G , Zeng Z F . Multiple soliton solutions, soliton-type solutions and rational solutions for the (3+1)-dimensional potential-YTSF equation. Indian J Pure App Math, 2014, 45: 989- 1002
doi: 10.1007/s13226-014-0100-9 |
39 |
Li Z T , Dai Z D . Exact periodic cross-kink wave solutions and breather type of two-solitary wave solutions for the (3+1)-dimensional potential-YTSF equation. Comput Math Appl, 2011, 61: 1939- 1945
doi: 10.1016/j.camwa.2010.07.055 |
[1] | 闫振亚 张鸿庆. 变形色散水波方程的Auto-Backlund变换、多孤子解和有理分式解[J]. 数学物理学报, 2000, 20(2): 210-215. |
[2] | 李志斌, 张善卿. 非线性波方程准确孤立波解的符号计算[J]. 数学物理学报, 1997, 17(1): 81-89. |
|