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HAMILTONIAN FORMULATION OF nonlinear water waves IN A TWO-FLUID SYSTEM

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Applied Mathematics and Mechanics(English Edition) 1999年第4期20卷 4-10页

作者：卢东强戴世强张宝善 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University 200072 Shanghai P R China

In this paper, it is dealt with that the Hamiltonian formulation of nonlinear water waves in a two_fluid system,which consists of two layers of constant_density incompressible inviscid fluid with a horizontal bottom,an interface and a free surface. The velocity potentials are expanded in power series of the vertical coordinate. By taking the kinetic thickness of lower fluid_layer and the reduced kinetic thickness of upper fluid_layer as the generalized displacements, choosing the velocity potentials at the interface and free surface as the generalized momenta and using Hamilton's principle, the Hamiltonian canonical equations for the system are derived with the Legendre transformation under the shallow water assumption. Hence the results for single_layer fluid are extended to the case of stratified fluid.

关键词： two_fluid system Hamilton's principle nonlinear water waves shallow water assumption Hamiltonian canonical equations

Numerical Simulation for nonlinear water waves Propagating along the Free Surface

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Journal of Applied Mathematics and Physics 2016年第5期4卷 930-938页

作者： Rabab Fadhel Al-Bar Department of Mathematics Faculty of Science Umm Al-Qura University Makkah KSA

The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation of the Korteweg-de Vries equations for solitons by using the method of multiple scale expansion. The proposed problem describes the behavior of the system for free surface between air and water in a nonlinear approach. To solve this problem, we use the well-known analytical method, namely, variational iteration method (VIM). The proposed method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. The proposed method provides a sequence of functions which may converge to the exact solution of the proposed problem. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves.

关键词： Variational Iteration Method nonlinear water waves Multiple Scale Korteweg-de Vries Equations Two Solitons Solution

Variational Principles and Hamiltonian Formulation for nonlinear water waves

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Advances in Manufacturing 1998年第3期 86-88页

作者： Doctoral Candidate: Zhang Baoshan Advisor: Prof.Dai Shiqiang

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关键词： Hamiltonian variational principle infinite dimensional Lie algebra nonlinear water waves KdV equation mKdV equation Hamiltonian canonical equation symplectic geometry

A Brief Summary of Finite Element Method Applications to nonlinear Wave-structure Interactions

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Journal of Marine Science and Application 2011年第2期10卷 127-138页

作者：王赤忠吴国雄 Department of Ocean Science and Engineering Zhejiang University Department of Mechanical Engineering University College London Torrington Place

We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.

关键词： finite element method (FEM) mesh generation nonlinear water waves wave-structure interactions

Rogue waves and Lump Solitons of the(3+1)-Dimensional Generalized B-type Kadomtsev–Petviashvili Equation for water waves

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Communications in Theoretical Physics 2017年第12期67卷 693-700页

作者：孙岩田播刘磊柴汉鹏袁玉强 State Key Laboratory of Information Photonics and Optical Communications and School of Science Beijing University of Posts and Telecommunications

In this paper, the(3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev–Petviashvili hierarchy reduction, we obtain the first-order,higher-order, multiple rogue waves and lump solitons based on the solutions in terms of the Gramian. The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again, while the first-order lump solitons propagate stably. Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented. Elastic interactions of several first-order lump solitons are also presented. We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones, while the interaction between the second-order lump solitons is inelastic.

关键词： nonlinear water waves Hirota method Kadomtsev–Petviashvili hierarchy reduction (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation rogue waves lump solitons