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Explicit solutions from residual symmetry of the boussinesq equation

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Chinese Physics B 2015年第3期24卷 19-25页

作者：刘希忠俞军任博 Institute of Nonlinear Science Shaoxing University

The Bcklund transformation related symmetry is nonlocal, which is hard to be applied in constructing solutions for nonlinear equations. In this paper, the residual symmetry of the boussinesq equation is localized to Lie point symmetry by introducing multiple new variables. By applying the general Lie point method, two main results are obtained： a new type of Backlund transformation is derived, from which new solutions can be generated from old ones; the similarity reduction solutions as well as corresponding reduction equations are found. The localization procedure provides an effective way to investigate interaction solutions between nonlinear waves and solitons.

关键词： boussinesq equation localization procedure residual symmetry symmetry reduction solution

A novel (G'/G)-expansion method and its application to the boussinesq equation

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Chinese Physics B 2014年第2期23卷 34-43页

作者： Md.Nur Alam Md.Ali Akbar Syed Tauseef Mohyud-Din Department of Mathematics Pabna University of Science and Technology Department of Applied Mathematics University of Rajshahi Department of Mathematics HITEC UniversityTaxila Cantt

In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.

关键词： (G'/G)-expansion method boussinesq equation solitary wave solutions auxiliary nonlinear ordinary differential equation

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Communications in Theoretical Physics 2001年第4期35卷 399-404页

作者： TANGXiao－Yan LINJi 等 DepartmentofAppliedPhysics ShanghaiJiaoTongUnioversityShanghai200030China CenterofNonlinearScience UniversityofScienceandTechnologyofChinaHefei230026CHina DepartmentofAppliedP

The direct method proposed by Clarkson and Kruskal is modified to obtain some conditional similarity solutions of a nonlinear physics model. Taking the -dimensional boussinesq equation as a simple example, six types o... 详细信息

关键词： conditional similarity reduction direct method boussinesq equation

Blow-up of solution for a generalized boussinesq equation

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Applied Mathematics and Mechanics(English Edition) 2007年第11期28卷 1437-1443页

作者：王艳萍郭柏灵 Department of Mathematics and Physics Zhengzhou Institute of Aeronautical Industry Management Institute of Applied Physics and Computational Mathematics P.O.Box 8009Beijing 100088P.R.China Institute of Applied Physics and Computational Mathematics

This paper studies the initial boundary value problem for a generalized Boussinese equation and proves the existence and uniqueness of the local generalized solution of the problem by using the Galerkin method. Moreov... 详细信息

关键词： boussinesq equation initial boundary value problem local solution blow-up of the solution

Simulating regular wave propagation over a submerged bar by boundary element method model and boussinesq equation model

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Chinese Physics B 2013年第2期22卷 308-313页

作者：李爽何海伦 Department of Ocean Science and Engineering Zhejiang University Key Laboratory of Ocean Circulation and Waves Chinese Academy of Sciences State Key Laboratory of Satellite Ocean Environment Dynamics Second Institute of OceanographySOA

Numerical models based on the boundary element method and boussinesq equation are used to simulate the wave transform over a submerged bar for regular *** the boundary-element-method model the linear element is used,and the integrals are computed by analytical *** boussinesq-equation model is the well-known FUNWAVE from the University of *** compare the numerical free surface displacements with the laboratory data on both gentle slope and steep slope,and find that both the models simulate the wave transform *** further compute the agreement indexes between the numerical result and laboratory data,and the results support that the boundary-element-method model has a stable good performance,which is due to the fact that its governing equation has no restriction on nonlinearity and dispersion as compared with boussinesq equation.

关键词： numerical wave tank boundary element method boussinesq equation

Modified asymptotic Adomian decomposition method for solving boussinesq equation of groundwater flow

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Applied Mathematics and Mechanics(English Edition) 2014年第4期35卷 481-488页

作者：陈芳刘青泉 Key Laboratory for Mechanics in Fluid Solid Coupling Systems Institute of Mechanics Chinese Academy of Sciences School of Applied Science Beijing Information Science and Technology University

The Adomian decomposition method （ADM） is an approximate analytic method for solving nonlinear equations. Generally, an approximate solution can be ob- tained by using only a few terms. However, in applications, we need to use it flexibly according to the real problem. In this paper, based on the ADM, we give a modified asymptotic Adomian decomposition method and use it to solve the nonlinear boussinesq equation describing groundwater flows. The example shows effectiveness of the modified asymptotic Adomian decomposition method.

关键词： groundwater flow boussinesq equation Adomian decomposition asymp-totic Adomian decomposition

Wave interaction for a generalized higher-dimensional boussinesq equation describing the nonlinear Rossby waves

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Journal of Oceanology and Limnology 2024年第5期42卷 1415-1424页

作者： Rong SU Penghao JI Xiaojun YIN College of Science Inner Mongolia Agricultural UniversityHohhot 010018China

Based on an algebraically Rossby solitary waves evolution model,namely an extended(2+1)-dimensional boussinesq equation,we firstly introduced a special transformation and utilized the Hirota method,which enable us to obtain multi-complexiton solutions and explore the interaction among the *** wave functions are then employed to infer the influence of background flow on the propagation of Rossby waves,as well as the characteristics of propagation in multi-wave running ***,we generated stereogram drawings and projection figures to visually represent these *** dynamical behavior of these solutions is thoroughly examined through analytical and graphical ***,we investigated the influence of the generalized beta effect and the Coriolis parameter on the evolution of Rossby waves.

关键词： Rossby wave boussinesq equation Complexiton solution Breather solution

A Generalization of F-Expansion Method and Its Application to （2＋l）-Dimensional boussinesq equation

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Communications in Theoretical Physics 2007年第5X期48卷 877-880页

作者： CHEN Jiang YANG Kong-Qing HE Hong-Sheng Lanzhou Institute of Physics Lanzhou University Lanzhou 730000 China Institute of Applied Physics Jimei University Xiamen 361021 China

A new generalized F-expansion method is introduced and applied to the study of the （2＋1）-dimensional boussinesq equation. The further extension of the method is discussed at the end of this paper.

关键词： F-expansion method Jacobi elliptic function boussinesq equation solitary wave solution

Novel Wronskian Solutions to boussinesq equation

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Communications in Theoretical Physics 2007年第4X期48卷 577-583页

作者： YAO Yu-Qin LIU Yu-Qing JI Jie CHEN Deng-Yuan Department of Mathematics Shanghai University Shanghai 200444 China

The new method for constructing the Wronskian entries is applied to the boussinesq equation. The novel Wronskian solutions to it are obtained, including solitons, rational solutions, Matveev solutions, and complexitons.

关键词： boussinesq equation Wronskiail technique rational solutions Matveev solutions complexitons