A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin–Bona–Mahony equations

Liang Gao; W. Xu; Y. Tang; G. Meng

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A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin–Bona–Mahony equations

机译：非线性色散广义Benjiamin–Bona–Mahony方程的新显式和精确解的广义代数方法

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摘要

Nonlinear dispersive generalized Benjiamin–Bona–Mahony equations are studied by using a generalized algebraic method. New abundant families of explicit and exact traveling wave solutions, including triangular periodic, solitary wave, periodic-like, soliton-like, rational and exponential solutions are constructed, which are in agreement with the results reported in other literatures, and some new results are obtained. These solutions will be helpful to the further study of the physical meaning and laws of motion of the nature and the realistic models. The proposed method in this paper can be further extended to the 2+1 dimensional and higher dimensional nonlinear evolution equations or systems of equations.

机译：使用广义代数方法研究非线性色散广义Benjiamin–Bona–Mahony方程。构造了新的丰富的显式和精确行波解族，包括三角周期，孤波，类周期，孤子类，有理和指数解，这与其他文献报道的结果一致，并且一些新的结果是获得。这些解决方案将有助于进一步研究自然界和现实模型的物理意义和运动规律。本文提出的方法可以进一步扩展到2 + 1维和更高维的非线性演化方程或方程组。

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来源
《Nonlinear Dynamics》 |2008年第4期|337-345|共9页
作者
Liang Gao; W. Xu; Y. Tang; G. Meng;
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作者单位

Department of Applied Mathematics Northwestern Polytechnical University Xi’an 710072 China;

Department of Applied Mathematics Northwestern Polytechnical University Xi’an 710072 China;

Department of Applied Mathematics Northwestern Polytechnical University Xi’an 710072 China;

Institute of Artificial Intelligence and Robotics Xi’an Jiaotong University Xi’an 710049 China;

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Nonlinear dispersive generalized Benjiamin—Bona–Mahony equations; Generalized algebraic method; New abundant families of explicit and exact solutions;

机译：非线性色散广义Benjiamin-Bona-Mahony方程;广义代数方法;新的显式和精确解类;

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专利

1. A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin-Bona-Mahony equations [J] . Gao L, Xu W, Tang Y, Nonlinear dynamics . 2008,第4期

机译：非线性色散广义Benjiamin-Bona-Mahony方程的新显式和精确解的广义代数方法
2. Exact traveling wave solutions to the Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation using the VIM combined with the improved generalized tanh-coth method [J] . Montri Torvattanabun, Sanoe Koonprasert Applied mathematical sciences . 2017,第61a64期

机译：VIM结合改进的广义tanh-coth方法求解Zakharov-Kuznetsov-Benjamin-Bona-Mahony非线性发展方程的精确行波解
3. New exact wave solutions of the variable-coefficient (1+1)-dimensional Benjamin-Bona-Mahony and (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations via the generalized exponential rational function method [J] . Ghanbari Behzad, Kuo Chun-Ku European Physical Journal Plus . 2019,第7期

机译：可变系数（1 + 1）的新精确波解，通过广义指数合理函数方法（2 + 1） - （2 + 1） - 二维不对称Nizhnik-Novikov-Veselov方程
4. On the exact explicit solutions of a generalized (2+1)-dimensional Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation [C] . Khadijo Rashid Adem, Chaudry Masood Khalique International Conference on Scientific Computing . 2013

机译：关于广义（2 + 1）的确切明确解决方案 - Dimensional Zakharov-Kuznetsov-Benjamin-Bona-Mahony方程
5. Existence and stability of solitary-wave solutions of equations of Benjamin-Bona-Mahony type. [D] . Zeng, Lei. 2000

机译：Benjamin-Bona-Mahony型方程的孤立波解的存在性和稳定性。
6. Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations [O] . Kamruzzaman Khan, M Ali Akbar, S M Rayhanul Islam -1

机译：（1 + 1）维非线性色散修正的Benjamin-Bona-Mahony方程和Klein-Gordon耦合方程的精确解
7. Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations [O] . 2014

机译：（1 + 1）维非线性色散修正的Benjamin-Bona-Mahony方程和Klein-Gordon耦合方程的精确解
8. Unstable solitary-wave solutions of the generalized Benjamin-Bona-Mahony equation [R] . McKinney, W R, Restrepo, J M, Bona, J L 1994

机译：广义Benjamin-Bona-mahony方程的不稳定孤波解

A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjiamin–Bona–Mahony equations

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