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Arbitrary Lagrangian‑Eulerian Discontinuous Galerkin Methods for kdv Type equations

Communications on Applied Mathematics and Computation 2022年第2期4卷 530-562页

作者： Xue Hong Yinhua Xia School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026AnhuiChina

In this paper,several arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)methods are presented for Korteweg-de Vries(kdv)type equations on moving *** on the L^(2) conservation law of kdv equations,we adopt the conservative and dissipative numerical fuxes for the nonlinear convection and linear dispersive terms,***,one conservative and three dissipative ALE-DG schemes are proposed for the *** invariant preserving property for the conservative scheme and the corresponding dissipative properties for the other three dissipative schemes are all presented and proved in this *** addition,the L^(2)-norm error estimates are also proved for two schemes,whose numerical fuxes for the linear dispersive term are both dissipative *** precisely,when choosing the approximation space with the piecewise kth degree polynomials,the error estimate provides the kth order of convergence rate in L^(2)-norm for the scheme with the conservative numerical fuxes applied for the nonlinear convection ***,the(k+1∕2)th order of accuracy can be proved for the ALE-DG scheme with dissipative numerical fuxes applied for the convection ***,a Hamiltonian conservative ALE-DG scheme is also presented based on the conservation of the Hamiltonian for kdv *** examples are shown to demonstrate the accuracy and capability of the moving mesh ALE-DG methods and compare with stationary DG methods.

关键词： Arbitrary Lagrangian-Eulerian discontinuous Galerkin methods kdv equations Conservative schemes Dissipative schemes Error estimates

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A UNIVERSAL IN TAILING WAVETRAIN GENERATION

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Journal of Hydrodynamics 2004年第5期16卷 603-607页

作者： XUZhao-ting SAMUELS.P.Shen QIAOFang-li InstituteofPhysicalOceanographyandPhysicalOceanographyLaboratory OceanUniversityofChinaQingdao266003China DepartmentofMathematicsScience UniversityofAlbertaEdmontonT6G2G1Canada KeyLaboratoryofMarineScienceandNumericalModeling TheFirstInstituteofOceanographyStateOceanicAdministrationQingdao266061China

A universal in tailing wave-train generation of forced soliton generationover topography is found theoretically as the flows are at the resonant points and it is examinedwith the numerical calculation of the corresponding fkdv e-quatioa From the comparisons, it is shownthat theoretical and numerical results on the invariance is in good agreement and the theory givenin this paper does not include the modulus truncation, any free constant and unknown function.

关键词： universal soliton tailing wave-train fkdv equation kdv equations

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Nonsingular Travelling Complexiton Solutions to a Coupled Korteweg-de Vries Equation

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Chinese Physics Letters 2008年第3期25卷 805-808页

作者：杨旭东阮航宇楼森岳 Department of Physics Ningbo University Ningbo 315211 Department of Physics Shanghai Jiao Tong University Shanghai 200030

A class of novel nonsingular travelling complexiton solutions to a coupled Korteweg-de Vries （kdv） equation is presented via the first step Darboux transformation of the complex kdv equation with nonzero seed soluti... 详细信息

关键词： kdv equations SOLITARY WAVES POSITON Nonsingular

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From decoupled integrable models to coupled ones via a deformation algorithm

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Communications in Theoretical Physics 2023年第10期75卷 38-44页

作者：杜文鼎孔德兴楼森岳 Zhejiang Qiushi Institute for Mathematical Medicine Hangzhou 311121China School of Physical Science and Technology Ningbo UniversityNingbo315211China

By using a reconstruction procedure of conservation laws of different models,the deformation algorithm proposed by Lou,Hao and Jia has been used to a new application such that a decoupled system becomes a coupled *** the new application to some decoupled systems such as the decoupled dispersionless Korteweg–de Vries(Kd V)systems related to dispersionless waves,the decoupled kdv systems related to dispersion waves,the decoupled kdv and Burgers systems related to the linear dispersion and diffusion effects,and the decoupled kdv and Harry–Dym(HD)systems related to the linear and nonlinear dispersion effects,we have obtained various new types of higher dimensional integrable coupled *** new models can be used to describe the interactions among different nonlinear waves and/or different effects including the dispersionless waves(dispersionless kdv waves),the linear dispersion waves(kdv waves),the nonlinear dispersion waves(HD waves)and the diffusion *** method can be applied to couple all different separated integrable models.

关键词： integrable systems deformation algorithm kdv equations higher dimensional integrable systems coupled and decoupled systems

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