CAI Niping.Bounded Traveling Wave Solutions of(4+1)Dimensional Fokas Equation[J].Journal of Chengdu University of Information Technology,2023,38(02):240-243.[doi:10.16836/j.cnki.jcuit.2023.02.017]
(4+1)维Fokas方程的有界行波解
- Title:
- Bounded Traveling Wave Solutions of(4+1)Dimensional Fokas Equation
- 文章编号:
- 2096-1618(2023)02-0240-04
- 关键词:
- (4+1)维Fokas方程; 动力系统; 周期波解; 孤波解
- Keywords:
- (4+1)dimensional Fokas equation; dynamical system; bell solitary wave solutions; periodic wave solutions
- 分类号:
- O192
- 文献标志码:
- A
- 摘要:
- 利用动力系统分岔的方法研究(4+1)维Fokas方程的有界行波解，获得不同参数情况下这个高维方程的行波系统的不同拓扑结构相图。这些相图清楚地展示了行波系统所有可能的有界轨道。通过复杂的椭圆积分，根据这些不同类型的轨道给出有界行波解，包括钟型孤立波解和周期波解。
- Abstract:
- In this paper, the bifurcation method of dynamical system is used to study the bounded traveling wave solutions of(4+1)dimensional Fokas equation. We obtain the different topological structure of the traveling wave solution of this higher dimensional equation with different parameters. These phase diagrams clearly show all bounded orbits of it. Calculating by complex elliptic integrals, bounded solutions of traveling waves are given according to these different types of orbits, including bell solitary wave solutions and periodic wave solutions.
参考文献/References:
[1] Hirota,Ryogo.Exact envelope-soliton solutions of a nonlinear wave equation[J].Journal of Mathematical Physics,1973,14(7):805-809.
[2] Lee J,Sakthivel R,Wazzan L.Exact traveling wave solutions of a higher-dimensional nonlinear evolution equation[J].Modern Physics Letters B,2010,24(10):1011-1021.
[3] Kim H,Sakthivel R.New exact traveling wave solutions of some nonlinear higher-dimensional physical models[J],Reports on Mathematical Physics,2012,70(1):39-50.
[4] He Y H.Exact solutions for(4+1)-dimensional nonlinear Fokas equation using extended F-expansion method and its variant[J].Mathematical Problems in Engineering,2014(8):1-11.
[5] Zhang S,Tian C,Qian W Y.Bilinearization and new multisoliton solutions for the(4+1)-dimensional Fokas equation[J].Pramana Journal of Physics,2016,86(6):1259-1267.
[6] Al-Amr M O,El-Ganaini S.New exact traveling wave solutions of the(4+1)-dimensional Fokas equation[J].Computers & Mathematics with Applications,2017,74(6):1274-1287.
[7] Gomez C A,Garzon G H,Hernandez R J C.On exact solutions for(4+1)-dimensional Fokas equation with variable coefficients[J].Advanced Studies in Theoretical Physics,2017,11(12):765-771.
[8] Wei L,Zhou Y,Liu Q.Traveling wave solutions of two types of generalized breaking soliton equations[J].Journal of Applied Analysis & Computation,2020,11(4).
[9] Zhou Y,Qian L.Bifurcation of travelling wave solutions for a(2+1)-dimensional nonlinear dispersive long wave equation[J].Applied Mathematics & Computation,2007,189(1):970-979.
[10] Wang L,Zhou Y,Liu Q.Traveling waves of the(3+1)-dimensional kadomtsev-petviashvili-boussinesq equation[J].Journal of Applied Analysis & Computation,2020,10(1):267-281.
[11] Li J,Zhu W,Chen G.Understanding Peakons,Periodic Peakons and Compactons via a Shallow Water Wave Equation[J].International Journal of Bifurcation & Chaos,2016,26(12):1650207.
[12] Zhou Y,Fan F,Liu Q.Bounded and unbounded traveling wave solutions of the(3+1)-dimensional Jimbo-Miwa equation[J].Results in Physics,2019,12:1149-1157.
[13] Li J,Chen G.Bifurcations of traveling wave solutions in a microstructured solid model[J].International Journal of Bifurcation and Chaos,2013,23(1):1-18.
[14] Li J,Chen G,Song J.Bifurcations and Dynamics of Traveling Wave Solutions for the Regularized Saint-Venant Equation[J].International Journal of Bifurcation and Chaos,2020,30(7):2050109.
[15] Qiao Z,Li J.Negative-order KdV equation with both solitons and kink wave solutions[J].Europhysics Letters,2011,94(5):50003.
[16] 张芷芬,丁同仁,黄文灶,等.微分方程定性理论[M].北京:科学出版社,1985:101-123.
备注/Memo
收稿日期:2022-05-19
基金项目:四川省科技厅资助项目(2021ZYD0009)