BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT

This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r^＊ which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if ｜r｜≥ r^＊; while they appear as damped oscillatory waves if ｜r｜ 〈 r^＊. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u（ξ） in the global phase portraits, and then obtain the approximate solutions （u（ξ）, H（ξ））. Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.

Simulating Long Waves in a Coifs Harbour 3D Physical Model Using Short Wave Spectra

This paper presents examples of field data of extreme seiche waves measured at Coffs Harbour by MHL and describes the generation and measuring methodology to detect and reduce seiche agitation in the Coifs Harbour boat ramp using a 3D physical model. The paper also discusses the techniques in investigating a short wave problem of stability in the same model where a long wave is simulated. Waves offshore of Coffs Harbour at 80 m depth have been recorded by MHL for a period of over 30 years. Long waves have been simultaneously measured in the harbour over a period of a decade. These data enabled the model to be verified on two dates （4/6/12, 5/9/14） when high long waves were recorded at the boat ramp harbour under storm and non-storm conditions. Long waves are generated in harbours due to group bounded long wave and surf beat or edge waves. The paper presents methodologies of generating long waves both numerically and by using physical models, and discusses the advantages and disadvantages of these generation techniques. Numerical modelling carried out using long period regular waves in a previous investigation predicted reductions up to 50% due to change of planform of the boat ramp harbour where an area next to the boat ramp was excavated and roughness elements introduced to dampen long periods. The 3D physical model simulated a 25% decrease in the long wave energy in the boat ramp when a suitable change in the planform was made. A 3D undistorted model of scale 1：58 was used in the investigation.

混凝土构件的有界性对应力波传播的影响及修正

将压电陶瓷片成对埋置在不同截面尺寸、不同长度的混凝土试件中,在输入信号幅值一定的情况下,通过改变信号主频考察输出信号幅值的变化情况,并拟合出各试验工况下的衰减系数函数。结果显示,试件有界性对应力波在混凝土介质中传播的衰减系数函数具有影响,这种影响随试件截面尺寸或传感器间距的增加而减弱。比较各试件工况下的试验结果,对应力波在无限大混凝土介质中传播的衰减系数函数的修正进行了研究。

受迫广义KdV－Burgers方程的周期行波解

讨论了一维广义ＫｄＶ－Ｂｕｒｇｅｒｓ方程的周期行波解，给出了解的有界性及估计式，进而讨论了解的存在性和唯一性。

二维广义非齐次KdV-Burgers方程的反周期行波解

讨论了二维广义非齐次KdV Burgers方程{ut+[f(u) ]x+αuxx+βuxxx} x+δuyy =gt≥ 0 ,x ,y∈R的反周期行波解的连续依赖性、解的有界性以及估计式 .

Ground State Nucleon, Dark Energy and Dark Matter

The recently introduced model of the nucleon as a system of three point particles predicts all characteristics of the proton and neutron with experimental precision only at condition that nucleon is the loosely bound state in system of deep potential wells. The model’s Hamiltonian contains ground state with the same parity and spin as the nucleon but with other different characteristics. Existence of this ground state nucleon means that the visible Universe is composed of excited matter. The direct transition between excited and ground states is strictly forbidden, however, stimulated emission can ignite such process. Most likely, corresponding conditions realize at supernova explosion. It is shown that presence of this matter, composed of ground state nucleons, in Universe gives the chance for consistent explanation of dark matter and dark energy phenomena.

Kinematic Relativity of Quantum Mechanics:Free Particle with Different Boundary Conditions

An investigation of origins of the quantum mechanical momentum operator has shown that it corresponds to the nonrelativistic momentum of classical special relativity theory rather than the relativistic one, as has been unconditionally believed in traditional relativistic quantum mechanics until now. Taking this correspondence into account, relativistic momentum and energy operators are defined. Schr&oumldinger equations with relativistic kinematics are introduced and investigated for a free particle and a particle trapped in the deep potential well.

Relativistic Dynamics of a Quantum System

In this paper, we examine quantum systems with relativistic dynamics. We show that for a successful description of these systems, the application of Galilei invariant nonrelativistic Hamiltonian is necessary. To modify this Hamiltonian to relativistic dynamics, we require precise relativistic kinetic energy operators instead of nonrelativistic ones for every internal (Jacobi) coordinate. Finally, we introduce and investigate the Schr&oumldinger equation with relativistic dynamics for two-particle systems with harmonic oscillator and Coulomb potentials.

Structure of Schrodinger’s Nucleon.Density Distributions and Zemach Momenta

The recently introduced Galilei invariant model of the nucleon as a system of three point particles, whose dynamics is governed by Schr?dinger equation, is applied for nucleon structure investigation. The obtained charge, magnetism, mass and point particles density distributions of the proton and neutron are in satisfactory agreement with known information about nucleon structure. The model predicts the third Zemach momentum of proton larger than the one obtained in dipole approximation and larger than following from electron-proton data analysis.

Structure of Schrodinger’s Nucleon:Elastic Form-Factors and Radii

The Galilei invariant model of the nucleon as a system of three point particles, whose dynamics is governed by Schr?dinger equation, after six Hamiltonian parameters fitting, predicts magnetic momenta, masses and charge radii of the proton and neutron with experimental precision. Now this model is applied in order to investigate nucleon charge, mass and magnetism distributions. The obtained electric and magnetic form factors at low values of momentum transfer are in satisfactory agreement with experimental information. The model predicts that neutron is a more compact system than proton.