一类非线性动力系统的孤立子波解

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1830-1837.

一类非线性动力系统的孤立子波解

欧阳成¹,莫嘉琪^2,*()

¹ 湖州师范学院理学院浙江湖州 313000
² 安徽师范大学数学与统计学院安徽芜湖 241003

收稿日期:2020-07-22 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 莫嘉琪 E-mail:mojiaqi@mail.ahnu.edu.cn
基金资助:
国家自然科学基金(11771005);浙江省自然科学基金(LY13A010005);浙江省自然科学基金(KJ2018A0964);浙江省自然科学基金(KJ2017A901)

The Solitary Wave Solution to a Class of Nonlinear Dynamic System

Cheng Ouyang¹,Jiaqi Mo^2,*()

¹ Faculty of Science, Huzhou University, Zhejiang Huzhou 313000
² School of Mathematics and Statistic, Anhui Normal University, Anhui Wuhu 241003

Received:2020-07-22 Online:2021-12-26 Published:2021-12-02
Contact: Jiaqi Mo E-mail:mojiaqi@mail.ahnu.edu.cn
Supported by:
the NSFC(11771005);the NSF of Zhejiang Province(LY13A010005);the NSF of Zhejiang Province(KJ2018A0964);the NSF of Zhejiang Province(KJ2017A901)

摘要/Abstract

摘要：

该文用泛函广义变分迭代方法，研究了一类非线性扰动动力系统.首先引入一个相应典型系统的孤立子波解.然后构造一组泛函广义变分式，求出Lagrange乘子，最后构造一组变分迭代关系式，由此便得到了原非线性扰动动力系统的渐近行波解.

关键词: 动力系统, 非线性, 孤立子波

Abstract:

Using the functional generalized variational iteration method, a class of nonlinear disturbed dynamic system was considered. First introduce solitary solution to a corresponding typical system. And then a set of functional generalized variation constructed, and Lagrange multiplier functions were solved. Finally, the generalized variational iteration was received. Thus, the asymptotic travelling wave solution to the original nonlinear disturbed generalized dynamic system was obtained

Key words: Dynamic system, Nonlinear, Solitary wave

中图分类号:

O175.29

欧阳成,莫嘉琪. 一类非线性动力系统的孤立子波解[J]. 数学物理学报, 2021, 41(6): 1830-1837.

Cheng Ouyang,Jiaqi Mo. The Solitary Wave Solution to a Class of Nonlinear Dynamic System[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1830-1837.

参考文献

1	McPhaden M J , Zhang D . Slowdown of the meridional overturning circulation in the upper Pacific ocean. Nature, 2002, 415, 603- 608
2	Gu D , Philander S G H . Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics. Science, 1997, 275 (7): 805- 807
3	马松华, 强继业, 方建平. (2+1)维Boiti-Leon-Pempinelli系统的混沌行为及孤立子波间的相互作用. 物理学报, 2007, 56, 620- 626
3	Ma S H , Qiang J Y , Fang J P . The interaction between solitons and chaotic behaviours of (2+1)-dimensional Boiti-Leon-Pempinelli system. Acta Phys Sin, 2007, 56, 620- 626
4	Loutsenko I . The variable coefficient Hele-Shaw problem, integrability and quadrature identities. Comm Math Phys, 2006, 268 (2): 465- 479
5	Gedalin M . Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description. Phys Plasmas, 1998, 5 (1): 127- 132
6	Parkes E J . Some periodic and solitary travelling-wave solutions of the short-pulse equation. Chaos Solitons Fractals, 2008, 38 (1): 154- 159
7	潘留仙, 左伟明, 颜家壬. Landau-Ginzburg-Higgs方程的微扰理论. 物理学报, 2005, 54 (1): 1- 5
7	Pan L X , Zuo W M , Yan J R . The theory of the perturbation for Landau-Ginzburg-Higgs equation. Acta Phys Sin, 2005, 54 (1): 1- 5
8	吴国将, 韩家骅, 史良马, 张苗. 一般变换下双Jacobi椭圆函数展开法及应用. 物理学报, 2006, 55 (8): 3858- 3863
8	Wu G J , Han J H , Shi L M , Zhang M . Double Jacobian elliptic function expansion method under a general function transform and its applications. Acta Phys Sin, 2006, 55 (8): 3858- 3863
9	马松华, 吴小红, 方建平, 郑春龙. (3+1)维Burgers系统的新精确解及其特殊孤立子波结构. 物理学报, 2008, 57 (1): 11- 17
9	Ma S H , Wu X H , Fang J P , Zheng C L . New exact solutions and special soliton structures for the (3+1)-dimensional Burgers system. Acta Phys Sin, 2008, 57 (1): 11- 17
10	李帮庆, 马玉兰. (G'/G)展开法和(2+1)维非对称Nizhnik-Novikov-Veselov系统的新精确解. 物理学报, 2009, 58 (7): 4373- 4378
10	Li B Q , Ma Y L . (G'/G)-expansion method and new exact solutions for (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov system. Acta Phys Sin, 2009, 58 (7): 4373- 4378
11	周振春, 马松华, 方建平, 任清褒. (2+1)维孤立子波系统的多孤立子波解和分形结构. 物理学报, 2010, 59 (11): 7540- 7545
11	Zhou Z C , Ma S H , Fang J P , Ren Q B . Multi-soliton solutions and fractal structures in a (2+1)-dimensional soliton system. Acta Phys Sin, 2010, 59 (11): 7540- 7545
12	高亮, 徐伟, 唐亚宁, 申建伟. 一类广义Boussinesq方程和Boussinesq-Burgers方程新的显式精确解. 物理学报, 2007, 56 (4): 1860- 1869
12	Gao L , Xu W , Tang Y Y , Shen J W . New explicit exact solutions of one type of generalized Boussinesq equations and the Boussinesq-Burgers equation. Acta Phys Sin, 2007, 56 (4): 1860- 1869
13	李向正, 李修勇, 赵丽英, 张金良. Gerdjikov-Ivanov方程的精确解. 物理学报, 2008, 57 (4): 2031- 2034
13	Ling X Z , Li X Y , Zhao L Y , Zhang J L . Exact solutions of Gerdjikov-Ivanov equation. Acta Phys Sin, 2008, 57 (4): 2031- 2034
14	Abid I , Jleli M , Trabelsi N . Weak solutions of quasilinear biharmonic problems with positive, increasing and convex nonlinearities. Anal Appl Singap, 2008, 6 (3): 213- 227
15	Hovhannisyan G , Vulanovi R . Stability inequalities for one-dimensional singular perturbation problems. Nonlinear Stud, 2008, 15 (4): 297- 322
16	Recke L , Omel'chenko O E . Boundary layer solutions to problems with infinite-dimensional singular perturbations. J Differential Equations, 2008, 245 (12): 3802- 2822
17	Graef J R , Kong L . Solutions of second order multi-point boundary value problems. Math Proc Camb Philo Soc, 2008, 145 (2): 489- 510
18	Mo J Q . Singular perturbation for a class of nonlinear reaction diffusion systems. Science in China Ser A, 1989, 32 (11): 1306- 1315
19	Mo J Q , Lin W T . Asymptotic solution for a class of sea-air oscillator model for El-Nino-southern oscillation. Chin Phys, 2008, 17 (1): 370- 372
20	Mo J Q , Lin W T . Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations. J Sys Sci & Complexity, 2008, 20 (1): 119- 128
21	Mo J Q , Lin Y H , Lin W T , Chen L H . Perturbed solving method for interdecadal sea-air oscillator model. Chin Geographical Sci, 2012, 22 (1): 42- 47
22	Mo J Q . Variational iteration solvi ng method for a class of generalized Boussinesq equation. Chin Phys Lett, 2009, 26 (6): 060202
23	Mo J Q . Homotopiv mapping solving method for gain fluency of a laser pulse amplifier. Science in China Ser G, 2009, 52 (7): 1007- 1010
24	Mo J Q , Lin W T , Wang H . Variational iteration solution of a sea-air oscillator model for the ENSO. Progress in Natural Science, 2007, 17 (2): 230- 232
25	欧阳成, 姚静荪, 石兰芳, 莫嘉琪. 一类尘埃等离子体孤子解. 物理学报, 2014, 63 (11): 110203
25	Ouyang C , Yao J S , Shi L F , Mo J Q . Solitary wave solution for a class of dusty plasma. Acta Phys Sin, 2014, 63 (11): 110203
26	欧阳成, 陈贤峰, 莫嘉琪. 广义扰动Nizhnik-Novikov-Veselov系统的孤波解的孤波解. 系统科学与数学, 2017, 37 (3): 908- 917
26	Ouyang C , Chen X F , Mo J Q . The solutions to solitary wave for generalized disturbed Nizhnik-Novikov-Veselov system. J Syst Sci Math Sci, 2017, 37 (3): 908- 917
27	欧阳成, 姚静荪, 石兰芳, 莫嘉琪. 一类广义鸭轨迹系统轨线的构造. 物理学报, 2012, 61 (3): 030202
27	Ouyang C , Yao J S , Shi L F , Mo J Q . Constructing path curve for a class of generalized phase tracks of canard system. Acta Phys Sin, 2012, 61 (3): 030202
28	欧阳成, 林万涛, 程荣军, 莫嘉琪. 一类厄尔尼诺海-气时滞振子的渐近解. 物理学报, 2013, 62 (6): 060201
28	Ouyang C , Lin W T , Cheng R J , Mo J Q . A class of asymptotic solution of sea-air time delay oscillator for the El Nino-southern oscillation mechanism. Acta Phys Sin, 2013, 62 (6): 060201
29	Ouyang C , Cheng L H , Mo J Q . Solving a class of burning disturbed problem with shock layer. Chin Phy B, 2012, 21 (5): 050203
30	de Jager E M , Jiang F R . The Theory of Singular Perturbation. Amsterdam: North-Holland Publishing Co, 1996
31	Barbu L , Morosanu G . Singularly Perturbed Boundary-Value Problems. Basel: Birkhauser, 2007
32	He J H . Variational iteration method–a kind of nonlinear analytical technique: Some examples. International J Non-linear Mechanics, 1999, 34 (4): 699- 708
33	He J H , Wu X H . Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitions & Fractals, 2006, 29 (1): 108- 113

[1]	刘鹏杰, 邵虎, 李佳宜, 董端端. 一个基于 BFGS 更新的惯性三项共轭梯度投影法[J]. 数学物理学报, 2025, 45(5): 1698-1710.
[2]	鹿高杰, 韩众, 刘露. 非局域反时空高阶非线性薛定谔方程的达布变换及其精确解[J]. 数学物理学报, 2025, 45(3): 767-775.
[3]	刘羽, 陈光淦, 李树勇. 随机 Kuramoto-Sivashinsky 方程行波解的非线性稳定[J]. 数学物理学报, 2025, 45(3): 790-806.
[4]	武文斌, 任雪, 张冉. 具有时滞的离散扩散疫苗接种模型的行波解[J]. 数学物理学报, 2025, 45(3): 858-874.
[5]	卢旭飞,焦昌华,杨静桦. $\mathbb{Z}_{p}$上仿射半群的动力系统[J]. 数学物理学报, 2025, 45(2): 305-320.
[6]	刘安淇,余婷,向长林. 一类双调和映照型偏微分方程组正则性研究[J]. 数学物理学报, 2025, 45(2): 408-417.
[7]	张倩. 拟线性薛定谔方程组在有界区域上的正规化解[J]. 数学物理学报, 2025, 45(1): 1-30.
[8]	娄瑜, 张翼. 推广的导数非线性薛定谔方程的单/双周期背景上的呼吸子和怪波及其碰撞解[J]. 数学物理学报, 2024, 44(6): 1511-1519.
[9]	连媛, 刘红军, 朱斌. 随机动力系统的 Weyl 平均等度连续性和 Weyl 平均敏感性[J]. 数学物理学报, 2024, 44(6): 1595-1606.
[10]	邱仰聪, 王其如. 一阶非线性时标动态方程的 Hyers-Ulam-Rassias 稳定性[J]. 数学物理学报, 2024, 44(2): 465-475.
[11]	吴泽康, 王晓丽, 韩文静, 李金红. 物理信息神经网络求解五阶 emKdV 方程的正反问题[J]. 数学物理学报, 2024, 44(2): 484-499.
[12]	简慧, 龚敏, 王莉. 带部分调和势的非齐次非线性 Schrödinger 方程的爆破解[J]. 数学物理学报, 2023, 43(5): 1350-1372.
[13]	沈旭辉,丁俊堂. 具有梯度源项和非线性边界条件的多孔介质方程组解的爆破[J]. 数学物理学报, 2023, 43(5): 1417-1426.
[14]	王贵贤,王秀彬,韩波. 聚焦 Kundu-Eckhaus 方程的反散射变换法: 阶跃振荡背景下的长时间渐进性[J]. 数学物理学报, 2023, 43(4): 1085-1122.
[15]	廖远康. 粘性依赖于密度的一维等熵可压缩 Navier-Stokes 方程组粘性激波的非线性稳定性[J]. 数学物理学报, 2023, 43(4): 1149-1169.