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Multisymplectic Scheme for the Improved boussinesq Equation

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Chinese Physics Letters 2013年第7期30卷 5-8页

作者： CAI Jia-Xiang QIN Zhi-Lin BAI Chuan-Zhi School of Mathematics Science Huaiyin Normal UniversityHuai'an 223300 Jiangsu Key Laboratory for NSLSCS School of Mathematics ScienceNanjing Normal UniversityNanjing 210046

We first note that the improved boussinesq equation has a multisymplectic *** on it,a multisymplectic scheme is *** relations analysis and linear stability analysis show that the proposed scheme has excellent *** resu... 详细信息

关键词： properties. structure. boussinesq

Dynamical Analysis and Exact Solutions of a New(2+1)-Dimensional Generalized boussinesq Model Equation for Nonlinear Rossby Waves

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Communications in Theoretical Physics 2019年第9期71卷 1054-1062页

作者： Quan-Sheng Liu Zai-Yun Zhang Rui-Gang Zhang Chuang-Xia Huang School of Mathematical Sciences Inner Mongolia UniversityHohhot010021China School of Aeronautics Science and Engineering Beihang UniversityBeijing100191China School of Mathematics Hunan Institute of Science and TechnologyYueyang414006China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Scienceand Technology Changsha410014China School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha410014China

In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta *** methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A383(2019) 514], we derive a new(2 + 1)-dimensional generalized boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.

关键词： generalized boussinesq model equation nonlinear Rossby waves dynamical analysis traveling wave solutions nonlinear perturbation expansions bifurcation theory of planar dynamical systems

Conservation Laws and Self-Consistent Sources for a Super-Classical-boussinesq Hierarchy

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Chinese Physics Letters 2011年第12期28卷 1-4页

作者： YU Fa-Jun College of Maths and Systematic Science Shenyang Normal UniversityShenyang 110034

The super-classical-boussinesq hierarchy with self-consistent sources is ***,infinitely many conservation laws for the integrable super-classical-boussinesq hierarchy are established.

关键词： boussinesq infinitely integrable

Parameter Extension and the Quasi-Rational Solution of a Lattice boussinesq Equation

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Chinese Physics Letters 2013年第4期30卷 1-4页

作者： NONG Li-Juan ZHANG Da-Jun SHI Ying ZHANG Wen-Ying Department of Mathematics Shanghai UniversityShanghai 200444

For a lattice boussinesq equation,we introduce a simple-parameter invertible transformation by which the equation is transformed into an extended *** new equation admits solitons and nonzero quasi-rational solutions,b... 详细信息

关键词： equation. boussinesq equation

Numerical study of edge waves using extended boussinesq equations

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Water Science and Engineering 2017年第4期10卷 295-302页

作者： Gang Wang Zhong-bin Sun Jun-liang Gao Xiao-zhou Ma Jiangsu Key Laboratory of Coast Ocean Resources Development and Environment Security(Hohai University) Nanjing 210098China Nanjing Hydraulic Research Institute Nanjing 210029China School of Naval Architecture and Ocean Engineering Jiangsu University of Science and TechnologyZhenjiang 212003China State Key Laboratory of Coastal and Offshore Engineering Dalian University of TechnologyDalian 116023China

An edge wave numerical model was developed based on extended boussinesq equations with the internal wave-generation method. The form of edge waves near a seawall was chosen as the input signal in order to avoid treatment of the moving shoreline on a sloping beach. As there was an energy transfer between different edge wave modes, not only the target mode but also other modes appeared in the simulations. Due to the nonlinear effect, the simulation results for mode-0 edge waves were slightly modulated by mode-1 and mode-2 waves. As the magnitudes of these higher-mode waves are not significantly related to those of the target mode, the internal wave-generation method in boussinesq equations can produce high-quality edge waves. The numerical model was used to investigate the nonlinear properties of standing edge waves, and the numerical results were in strong agreement with theory.

关键词： Edge waves boussinesq equations Internal wave-generation method Nonlinear wave interaction

Multiple Soliton Solutions of Alice–Bob boussinesq Equations

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Chinese Physics Letters 2019年第5期36卷 22-26页

作者： Hui Li S.Y.Lou School of Physical Science and Technology Ningbo UniversityNingbo 315211 Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062

Three Alice-Bob boussinesq(ABB) nonlocal systems with shifted parity■, delayed time reversal■ and ■ nonlocalities are investigated. The multi-soliton solutions of these models are systematically found from the ■ symmetry reductions of a coupled local boussinesq system. The result shows that for ABB equations with ■ nonlocality, an odd number of solitons is prohibited. The solitons of the ■ nonlocal ABB and ■ nonlocal ABB equations must be paired, while any number of solitons is allowed for the ■ nonlocal ABB system. t-breathers, x-breathers and rogue waves exist for all three types of nonlocal ABB *** particular, different from classical local cases, the first-order rogue wave can have not only four leaves but also five and six leaves.

关键词： ABB Bob boussinesq Equations Multiple Soliton Solutions of Alice

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE boussinesq EQUATIONS

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Acta Mathematica Scientia 2019年第1期39卷 165-179页

作者： Feng CHENG Chao jiang XU Hubei Key Laboratory of Applied Mathematics School of Mathematics and Statistics Hubei University School of Mathematics and Statistics Wuhan University Universite de Rouen CNRS UMR 6085 Laboratoire de Mathématiques

In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H^1 -solution to the incompressible boussinesq equations in periodic domain is analytic for any positive time. So the incompressible boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

关键词： analyticity smoothing effect of solutions boussinesq equation

One-dimensional numerical models of higher-order boussinesq equations with high dispersion accuracy

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Acta Oceanologica Sinica 2003年第2期22卷 287-300页

作者： ZouZhili WangTao ZhangXiaoli DarrenSpratt StateKeyLaboratoryofCoastalandOffshoreEngineering DepartmentofCivilEngineeringDalianUniversityofTechnologyDalian116024China CivilandEnvironmentalEngineering UniversityofIllinoisatUrbana-ChampaignChampaignUSA

Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of the wave propagation model of higher-order boussinesq equations derived by Zou (2000, Ocean Engineering, 27, 557 - 575) is investigated. Physical experiments are conducted; three different front slopes (1:10, 1 = 5 and 1:2) of the shelf are set-up in the experiment and their effects on the wave propagation are investigated. Comparisons of the numerical results with test data are made and the higher-order boussinesq equations agree well with the measurements since the dispersion of the model is of high accuracy. The numerical results show that the good results can also be obtained for the steep-slope cases although the mild-slope assumption is employed in the derivation of the higher-order terms in the higher-order boussinesq equations.

关键词： Water waves boussinesq nonlinear dispersion

On the Global Well-Posedness of 3-D boussinesq System with Variable Viscosity

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Chinese Annals of Mathematics,Series B 2019年第5期40卷 643-688页

作者： Hammadi ABIDI Ping ZHANG Departement de Mathématiques Facultédes Sciences de Tunis Universitéde Tunis El Manar2092Tunis Academy of Mathematics&Systems Science and Hua Loo-Keng Key Laboratory of Mathematics Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

In this paper, the authors first consider the global well-posedness of 3-D boussinesq system, which has variable kinematic viscosity yet without thermal conductivity and buoyancy force, provided that the viscosity coefficient is sufficiently close to some positive constant in L∞and the initial velocity is small enough in B3,10(R3). With some thermal conductivity in the temperature equation and with linear buoyancy force θe3 on the velocity equation in the boussinesq system, the authors also prove the global well-posedness of such system with initial temperature and initial velocity being sufficiently small in L1(R3)and B3,10(R3) respectively.

关键词： boussinesq systems Littlewood-Paley theory Variable viscosity Maximal regularity of heat equation