A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

doi:10.1088/1674-1056/17/2/008

中国物理B ›› 2008, Vol. 17 ›› Issue (2): 399-402.doi: 10.1088/1674-1056/17/2/008

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

潘军廷, 龚伦训

School of Science, Guizhou Noal University, Guiyang 550001, China

收稿日期:2007-01-22 修回日期:2007-03-07 出版日期:2008-02-20 发布日期:2008-02-20
基金资助:
Project supported by the Science and Technology Foundation of Guizhou Province, China (Grant No 20072009).

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

Pan Jun-Ting(潘军廷) and Gong Lun-Xun(龚伦训)^†

School of Science, Guizhou Noal University, Guiyang 550001, China

Received:2007-01-22 Revised:2007-03-07 Online:2008-02-20 Published:2008-02-20
Supported by:
Project supported by the Science and Technology Foundation of Guizhou Province, China (Grant No 20072009).

摘要/Abstract

摘要： Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin--Bona--Mahony (mBBM) model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.

Abstract: Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation, and by converting it into a new expansion form, this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to modified Benjamin--Bona--Mahony (mBBM) model, and some new exact solutions to the system are obtained. The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.

Key words: nonlinear evolution equations, new expansion method, mBBM model, exact solutions

中图分类号: (Ordinary differential equations)

02.30.Hq

02.10.-v (Logic, set theory, and algebra) 05.45.-a (Nonlinear dynamics and chaos)

潘军廷, 龚伦训. A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model[J]. 中国物理B, 2008, 17(2): 399-402.

Pan Jun-Ting(潘军廷) and Gong Lun-Xun(龚伦训). A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model[J]. Chin. Phys. B, 2008, 17(2): 399-402.

[1]	Bin He(何斌) and Qing Meng(蒙清). Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel-Korteweg-de Vries equation[J]. 中国物理B, 2021, 30(6): 60201-060201.
[2]	师利娟, 温振庶. Dynamics of traveling wave solutions to a highly nonlinear Fujimoto-Watanabe equation[J]. 中国物理B, 2019, 28(4): 40201-040201.
[3]	温振庶, 师利娟. Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation[J]. 中国物理B, 2018, 27(9): 90201-090201.
[4]	王金环, 许玉玲, 张建, 杨德东. Time-varying formation for general linear multi-agent systems via distributed event-triggered control under switching topologies[J]. 中国物理B, 2018, 27(4): 40504-040504.
[5]	金世欣, 张毅. Generalized Chaplygin equations for nonholonomic systems on time scales[J]. 中国物理B, 2018, 27(2): 20502-020502.
[6]	韩青爽, 陈帝伊, 张浩. Bursting oscillations in a hydro-turbine governing system with two time scales[J]. 中国物理B, 2017, 26(12): 128202-128202.
[7]	鲍江宏, 陈丹丹. Coexisting hidden attractors in a 4D segmented disc dynamo with one stable equilibrium or a line equilibrium[J]. 中国物理B, 2017, 26(8): 80201-080201.
[8]	张翔, 王金环, 杨德东, 徐勇. Tracking consensus for nonlinear heterogeneous multi-agent systems subject to unknown disturbances via sliding mode control[J]. 中国物理B, 2017, 26(7): 70501-070501.
[9]	R Saravanakumar, M Syed Ali. Robust H_∞ control for uncertain Markovian jump systems with mixed delays[J]. 中国物理B, 2016, 25(7): 70201-070201.
[10]	Hakan Ciftci, H F Kisoglu. Application of asymptotic iteration method to a deformed well problem[J]. 中国物理B, 2016, 25(3): 30201-030201.
[11]	F M Abbasi, M Mustafa, S A Shehzad, M S Alhuthali, T Hayat. Analytical study of Cattaneo-Christov heat flux model for a boundary layer flow of Oldroyd-B fluid[J]. 中国物理B, 2016, 25(1): 14701-014701.
[12]	刘期怀, 邢明燕, 李新祥, 王超. Unstable and exact periodic solutions of three-particles time-dependent FPU chains[J]. 中国物理B, 2015, 24(12): 120401-120401.
[13]	M. Syed Ali, R. Saravanakumar. Robust H_∞ control of uncertain systems with two additive time-varying delays[J]. 中国物理B, 2015, 24(9): 90202-090202.
[14]	M. Syed Ali, R. Saravanakumar. Augmented Lyapunov approach to H_∞ state estimation of static neural networks with discrete and distributed time-varying delays[J]. 中国物理B, 2015, 24(5): 50201-050201.
[15]	M. Syed Ali, R. Saravanakumar. Improved delay-dependent robust H_∞ control of an uncertain stochastic system with interval time-varying and distributed delays[J]. , 2014, 23(12): 120201-120201.

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

A new expansion method of first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term and its application to mBBM model

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0