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 共查询到20条相似文献,搜索用时 15 毫秒
1.
Huang  Qian-Min  Gao  Yi-Tian 《Nonlinear dynamics》2017,89(4):2855-2866
Nonlinear Dynamics - Under investigation in this paper is a $$(2 + 1)$$ -dimensional extended shallow water wave equation. Bilinear form is obtained via the generalized dependent variable...  相似文献   

2.
Osman  M. S.  Machado  J. A. T. 《Nonlinear dynamics》2018,93(2):733-740
Nonlinear Dynamics - A variety of new types of nonautonomous combined multi-wave solutions of the ( $$2+1$$ )-dimensional variable coefficients KdV equation is derived by means of the generalized...  相似文献   

3.
Lv  Jianqing  Bilige  Sudao 《Nonlinear dynamics》2017,90(3):2119-2124
Nonlinear Dynamics - In this paper, we obtained a kind of lump solutions of ( $$2+1$$ )-dimensional bSK equation with the assistance of Mathematica by using the Hirota bilinear method. These lump...  相似文献   

4.
Li  Long-Xing 《Nonlinear dynamics》2022,108(2):1627-1640
Nonlinear Dynamics - A ( $$3+1$$ )-dimensional generalized shallow water waves equation is investigated with different methods. Based on symbolic computation and Hirota bilinear form, N-soliton...  相似文献   

5.
Li  Liu-Qing  Gao  Yi-Tian  Hu  Lei  Jia  Ting-Ting  Ding  Cui-Cui  Feng  Yu-Jie 《Nonlinear dynamics》2020,100(3):2729-2738
Nonlinear Dynamics - In this paper, we investigate a ( $$2+1$$ )-dimensional Sawada–Kotera (SK) equation for the atmosphere, rivers, lakes, oceans, as well as the conformal field and...  相似文献   

6.
Sun  Yan  Tian  Bo  Yuan  Yu-Qiang  Du  Zhong 《Nonlinear dynamics》2018,94(4):3029-3040
Nonlinear Dynamics - Under investigation in this work is a $$(2+1)$$ -dimensional Davey–Stewartson system, which describes the surface water wave packets of finite depth. With respect to the...  相似文献   

7.
Chen  Yiren  Liu  Zhengrong 《Nonlinear dynamics》2017,87(2):1069-1080
Nonlinear Dynamics - In this paper, we consider the (3 $$+$$ 1)-dimensional water wave equation $$u_{yzt}+u_{xxxyz}-6u_{x}u_{xyz}-6u_{xy}u_{xz}=0.$$ Based on Bell polynomials, we obtain its Hirota...  相似文献   

8.
Zhang  Yan  Liu  Yinping  Tang  Xiaoyan 《Nonlinear dynamics》2018,93(4):2533-2541
Nonlinear Dynamics - This paper aims at computing M-lump solutions for the $$(3+1)$$ -dimensional nonlinear evolution equation. These solutions in all directions decline to an identical state...  相似文献   

9.
In the present paper,a general solution involving three arbitrary functions for the generalized(2+1)dimensional KdV-mKdV equation,which is derived fromthe generalized(1+1)-dimensional KdV-mKdV equation,is first introduced by means of the Wiess,Tabor,Carnevale(WTC) truncation method.And then multisymplectic formulations with several conservation lawstaken into account are presented for the generalized(2+1)dimensional KdV-mKdV equation based on the multisymplectic theory of Bridges.Subsequently,in order tosimulate the periodic wave solutions in terms of rationalfunctions of the Jacobi elliptic functions derived from thegeneral solution,a semi-implicit multi-symplectic schemeis constructed that is equivalent to the Preissmann scheme.From the results of the numerical experiments,we can conclude that the multi-symplectic schemes can accurately simulate the periodic wave solutions of the generalized(2+1)dimensional KdV-mKdV equation while preserve approximately the conservation laws.  相似文献   

10.
Zhou  Tian-Yu  Tian  Bo  Chen  Yu- Qi  Shen  Yuan 《Nonlinear dynamics》2022,108(3):2417-2428
Nonlinear Dynamics - Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2 $$+$$ 1)-dimensional...  相似文献   

11.
Zhao  Zhonglong  Han  Bo 《Nonlinear dynamics》2018,94(1):461-474
Nonlinear Dynamics - In this paper, the truncated Painlevé expansion is employed to derive a Bäcklund transformation of a ( $$2+1$$ )-dimensional nonlinear system. This system can be...  相似文献   

12.
IntroductionSolitonisacomplicatedmathematicalstructurebasedonthenonlinearevolutionequation[1].Thoughsolitonstructuresandpropertiesofthe ( 1 + 1 )_dimensionalnonlinearphysicalmodelshavebeenstudiedwellandunderstoodfurther,thesolitonstructuresinhigherspatialdi…  相似文献   

13.
Wang  Chuanjian  Fang  Hui  Tang  Xiuxiu 《Nonlinear dynamics》2019,95(4):2943-2961
Nonlinear Dynamics - In this paper, we are mainly concerned with the (2+1)-dimensional generalized Korteweg–de Vries equation in fluid dynamics. Based on the translation transformation and...  相似文献   

14.
Gao  Li-Na  Zi  Yao-Yao  Yin  Yu-Hang  Ma  Wen-Xiu    Xing 《Nonlinear dynamics》2017,89(3):2233-2240
Nonlinear Dynamics - In this paper, a $$(3+1)$$ -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund...  相似文献   

15.
In this paper the concept of pseudopotential is generalized to non-linear evolution equations in 2 + 1 dimensions. If the equations satisfied by the pseudopotential are of a Riccati-type in the x-variable, it is shown how to obtain both the generalized AKNS system and the auto-Bäcklund transformation for the corresponding non-linear evolution equation. Several examples are given: Kadomtsev-Petviashvili, modified Kadomtsev-Petviashvili, (2 + 1 dim.)-Harry-Dym, and (2 + 1 dim.)-Sawada-Kotera equations.  相似文献   

16.
Wang  Lili  Luan  Zitong  Zhou  Qin  Biswas  Anjan  Alzahrani  Abdullah Kamis  Liu  Wenjun 《Nonlinear dynamics》2021,104(3):2613-2620
Nonlinear Dynamics - The (2+1)-dimensional generalized coupled nonlinear Schrödinger equation with the four-wave mixing (FWM) term is studied in this paper, which describes the optical...  相似文献   

17.
Journal of Dynamics and Differential Equations - Let $$\text {Homeo}_{+}(\mathbb {S}^1)$$ denote the group of orientation preserving homeomorphisms of the circle $$\mathbb {S}^1$$ . A subgroup G of...  相似文献   

18.
Osman  M. S. 《Nonlinear dynamics》2017,87(2):1209-1216
Nonlinear Dynamics - In this paper, the generalized unified method is used to construct multi-rational wave solutions of the ( $$2 + 1$$ )-dimensional Kadomtsev–Petviashvili equation with...  相似文献   

19.
By means of the auxiliary ordinary differential equation method, we have obtained many solitary wave solutions, periodic wave solutions and variable separation solutions for the (2+1)-dimensional KP equation. Using a mixed method, many exact solutions have been obtained.  相似文献   

20.
Nonlinear Dynamics - We study two (3 $$+$$ 1)-dimensional generalized equations, namely the Kadomtsev–Petviashvili–Boussinesq equation and the B-type...  相似文献   

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