广义的(3+1)维Kadomtsev-Petviashvili方程的动力分析及其行波解

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 501-509.

广义的(3+1)维Kadomtsev-Petviashvili方程的动力分析及其行波解

张雪^1,²(),孙峪怀^1,*()

¹ 四川师范大学数学科学学院成都 610066
² 西南交通大学希望学院成都 610400

收稿日期:2017-01-25 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 孙峪怀 E-mail:1443773002@qq.com;sunyuhuai63@163.com
作者简介:张雪, 1443773002@qq.com
基金资助:
国家自然科学基金(11371267);四川省教育厅自然科学重点基金(2012ZA135)

Dynamical Analysis and Traveling Wave Solutions for Generalized (3+1)-Dimensional Kadomtsev-Petviashvili Equation

Xue Zhang^1,²(),Yuhuai Sun^1,*()

¹ College of Mathematics Science, Sichuan Normal University, Chengdu 610066
² Southwest Jiaotong University Hope College, Chengdu 610400

Received:2017-01-25 Online:2019-06-26 Published:2019-06-27
Contact: Yuhuai Sun E-mail:1443773002@qq.com;sunyuhuai63@163.com
Supported by:
Sponsored by the NSFC(11371267);the SCNSF(2012ZA135)

摘要/Abstract

摘要：

运用拟设方法和动力系统分支方法，获得了广义（3+1）维Kadomtsev-Petviashvili方程的奇异孤子解及其行波解.

关键词: 广义的(3+1)维Kadomtsev-Petviashvili方程, 拟设方法, 分支方法, 分支相图, 行波解

Abstract:

Dynamical analysis and explicit solutions for generalized (3+1)-dimension Kadomtsev-Petviashvili equation have been carried out. The singular solution is obtained by the ansatz method, the bifurcation phase portraits and corresponding explicit solution are also constructed by the approach of dynamical analysis.

Key words: Generalized (3+1)-dimension Kadomtsev-Petviashvili equation, Ansatz method, Bifurcation analysis, Phase portraits, Traveling wave solutions

中图分类号:

O175.29

张雪,孙峪怀. 广义的(3+1)维Kadomtsev-Petviashvili方程的动力分析及其行波解[J]. 数学物理学报, 2019, 39(3): 501-509.

Xue Zhang,Yuhuai Sun. Dynamical Analysis and Traveling Wave Solutions for Generalized (3+1)-Dimensional Kadomtsev-Petviashvili Equation[J]. Acta mathematica scientia,Series A, 2019, 39(3): 501-509.

图/表 4

参考文献 26

1	Adair D , Jaeger M . Simulation of tapered rotating beams with centrifugal stiffening using the adomian decomposition method. Applied Mathematical Modelling, 2016, 40: 3230- 3241 doi: 10.1016/j.apm.2015.09.097
2	Hasseine A , Bart H J . Adomian decomposition method solution of population balance equations for aggregation, nucleation, growth and breakup processes. Applied Mathematical Modelling, 2015, 39: 1975- 1984 doi: 10.1016/j.apm.2014.09.027
3	Aski F S , Seyed J N , Mohammadian E , Asgari A . Application of adomian decomposition method for micropolor flow in a porous channel. Propulsion and Power Research, 2014, 3: 15- 21 doi: 10.1016/j.jppr.2014.01.004
4	Reza M . Numerical solution of the Laplace equation in annulus by Adomian decomposition method. Chaos Solitons and Fractals, 2008, 36: 138- 143 doi: 10.1016/j.chaos.2006.06.016
5	Ein M S . Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics. Chaos Solitons and Fractals, 2008, 35: 420- 422 doi: 10.1016/j.chaos.2007.06.121
6	Biswas A , Yildirim A , Hayat T , et al. Soliton perturbation theory for the generalized klein-gordon equation with full nonlinearity. Proceedings of the Romanian Academy, 2012, 13: 32- 41
7	Hutchinson A J , Mason D P . Lie symmetry methods applied to the turbulent wake of a symmetric self-propelled body. Applied Mathematical Modelling, 2016, 40: 3062- 3080 doi: 10.1016/j.apm.2015.10.007
8	Song M , Rong Z L , Essaid Z , Anjan B . Singular solitons and bifurcation analysis of quadratic nonlinear klein-gordon equation. Applied Mathematical Information Science, 2013, 4: 1333- 1340
9	Triki H , Yildirim A , Hayat T , et al. Topological and non-topological soliton solutions of the bretherton equation. Proceedings of the Romanian Academy, 2012, 13: 688- 696
10	Triki H , Crutcher S , Yildirim A , et al. Bright and dark solitons of the modified complex ginzburg-landau equation with parabolic and dualpower law nonlinearity. Romanian Reports in Physics, 2012, 64: 367- 380
11	Chang S H . Convergence of variational iteration method applied two-point diffusion problems. Applied Mathematical Modelling, 2016, 40: 6805- 6810 doi: 10.1016/j.apm.2016.02.024
12	Salkuyeh D K , Tavakoli A . Interpolated variational iteration method for initial value problems. Applied Mathematical Modelling, 2016, 40: 3979- 3990 doi: 10.1016/j.apm.2015.10.037
13	Khuri S A , Sayfy A . A novel fixed point scheme proper setting of variational iteration method for BVPs. Applied Mathematical Letter, 2015, 48: 75- 84 doi: 10.1016/j.aml.2015.03.017
14	Concli F , Gorla C . Numerical modeling of the power losses in geared transmissions: Windage, churning and cavitation simulations with a new integrated approach that drastically reduces the computational effort. Tribology International, 2016, 103: 58- 68 doi: 10.1016/j.triboint.2016.06.046
15	Zhang M X , Li Y X , Li Y , et al. Numerical simulations on the effect of sloshing on liquid flow maldistribution of randomly packed column. Applied Thermal Engineering, 2017, 112: 585- 594 doi: 10.1016/j.applthermaleng.2016.10.049
16	Cheshmehzangi A . Multi-spatial environmental performance evaluation towards integrated urban design: A procedural approach with computational simulations. Journal of Cleaner Production, 2016, 139: 1085- 1093 doi: 10.1016/j.jclepro.2016.08.151
17	Kadomtsev B B , Petviashvili V . On the stability of solitary waves in weakly dispersive media. Soviet Physics Doklady, 1970, 15: 539- 541
18	Li D , Lin J , Liu X . Soliton deflexion for (1+3)-D Kadomtsev-Petviashvili equation. Commun Nonlinear Sci Numer Simul, 2009, 14: 3548- 3553 doi: 10.1016/j.cnsns.2009.02.007
19	Dorizzi B , Grammaticos B , Ramani A , Winternitz P . Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable?. Journal of Mathematical Physics, 1986, 27: 2848- 2852 doi: 10.1063/1.527260
20	Lv N , Mei J Q , Zhang H Q . New explicit solutions for(3+1)-dimensional Kadomtsev-Petviashvili (KP) equation. International Journal of Nonlinear Science, 2011, 11: 506- 512
21	Peng Y Z , Krishnan E V . Exact travelling wave solutions to the (3+1)-dimensional Kadomtsev-Petviashvili equation. Acta Physical Polonica, 2005, 108: 421- 428 doi: 10.12693/APhysPolA.108.421
22	Alam M N , Akbar M A . Application of new generalized $(\frac{{G'}}{G})$-expansion method to the (3+1)-dimensional Kadomtsev-Petviashvili equation. Italian Journal of Pure and Applied Mathematics, 2016, 36: 1- 14
23	Yang R . Bifurcation analysis of a diffusive predator-prey system with Crowley-Martin functional response and delay. Chaos Solitons and Fractals, 2017, 95: 131- 139 doi: 10.1016/j.chaos.2016.12.014
24	Tang X , Song Y . Bifurcation analysis and Turing instability in a diffusive predator-prey model with herd behavior and hyperbolic mortality. Chaos Solitons and Fractals, 2015, 81: 303- 314 doi: 10.1016/j.chaos.2015.10.001
25	Chow S N , Hale J K . Method of Bifurcation Theory. New York: Springer-Verlag, 1982
26	Guckenheimer J , Homes P . Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. New York: Springer-Verlag, 1999

[1]	邹霞, 吴事良. 一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解[J]. 数学物理学报, 2018, 38(3): 496-513.
[2]	郭庭光, 徐志庭. 带有扩散项和接种的传染病模型的行波解[J]. 数学物理学报, 2017, 37(6): 1129-1147.
[3]	娄翠娟, 杨茵. 一类经典趋化性模型行波解的存在性[J]. 数学物理学报, 2015, 35(6): 1044-1058.
[4]	匡杰,王泽军. 非齐次Burgers方程周期解的大时间行为[J]. 数学物理学报, 2015, 35(1): 1-14.
[5]	马满军, 胡建超, 杨道明. 具非线性扩散一般反应系统的行波解存在性[J]. 数学物理学报, 2012, 32(1): 113-125.
[6]	梁飞, 高洪俊. 非局部时滞反应扩散方程行波解的存在性[J]. 数学物理学报, 2011, 31(5): 1273-1281.
[7]	智红燕, 陈勇, 张鸿庆. 广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解[J]. 数学物理学报, 2005, 25(7): 956-964.
[8]	刘春平. 一些非线性发展方程的显式行波解[J]. 数学物理学报, 2004, 4(6): 661-668.
[9]	康东升. 一个反应扩散方程的显式波前解与一个平面三次微分系统的全局分析[J]. 数学物理学报, 1998, 18(S1): 1-12.