随机Benjamin-Ono 方程初值问题及对河口区域生物分布的应用

该文对具梯度耦合噪声的随机Benjamin-Ono 方程（以下简记为B-O方程）的初值问题导出了解得积分表达式，并将它应用于河口区域生物分布问题，得到了一维空间的分布表达式。     

Constructing Space for Science at the Royal Institution of Great Britain

Those who have worked in the Royal Institution of Great Britain have, since its foundation in 1799, made significant contributions to scientific knowledge, to its practical application, and to its communication to a wide variety of audiences. Such work cannot be carried out in an architectural vacuum, and in this paper we examine how the buildings of the Royal Institution, 20 and 21 Albemarle Street in central London, have shaped the work undertaken within its walls and how, on a number of occasions, the buildings have been reconfigured to take account of the evolving needs of scientific research and communication. This paper is based on the Conservation Plan of the Royal Institution that we wrote during 2003. The Conservation Plan did not examine the land owned by the Royal Institution to the north (i.e., 22 and 23 Albemarle Street; for this area see Richard Garnier, “Grafton Street, Mayfair,” Georgian Group Journal 13 (2003), 210–272), but it did discuss 18 and 19 Albemarle Street. In this paper we concentrate on the core Royal Institution buildings at 20 and 21 Albemarle Street. Other studies of the relationship of architecture,space, and science include Crosbie Smith and Jon Agar, ed., Making Space for Science: Territorial Themes in the Shaping of Knowledge (Basingstoke: Macmillan, 1997); Peter Galison and Emily Thompson, ed., The Architecture of Science (Cambridge, Mass.: MIT Press, 1999); and Sophie Forgan,“The architecture of science and the idea of a university,” Studies in History and Philosophy of Science 20 (1989), 405–434. Frank A.J.L. James is Professor of the History of Science at the Royal Institution; he has written widely on the history of nineteenth-century science in its social and cultural contexts and is editor of the Correspondence of Michael Faraday. He is President of the British Society for the History of Science. Anthony Peers is an Associate of Rodney Melville and Partners where he works in the field of building conservation as an architectural historian. He is a Council member of the Ancient Monument Society.     

On the stability of the solitary waves to the rotation Benjamin‐Ono equation

In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin‐Ono equation. By solving a minimization problem on the line, we construct a family of even travelling waves ψ_c,γ. We then prove the uniqueness of even ground states associated with large speed and their orbital stability. Note that this improves the results in Esfahani and Levandosky, where only the stability of the set of ground states is proven.     

修正的BBM方程新的精确解

应用进一步修正的简单方程法对修正的 Benjamin -Bona -Mahoney (mBBM )方程进行求解,给出了mBBM方程新的精确类孤波解,取定某些参数值,便可得到精确孤波解.这种方法也可用于寻找其它常系数以及变系数非线性发展方程(组)的精确解,具有一定的普适性.     

On well-posedness for some dispersive perturbations of Burgers' equation

We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin–Ono equation

${?}_{t}u?D_x^{\alpha }{?}_{x}u={?}_x(u^2),0<\alpha \le 1,$

is locally well-posed in $H^s(\mathbb{R})$ when $s>s_{\alpha }:=\frac{3}{2}?\frac{5\alpha }{4}$. As a consequence, we obtain global well-posedness in the energy space $H^{\frac{\alpha }{2}}(\mathbb{R})$ as soon as $\frac{\alpha }{2}>s_{\alpha }$, i.e. $\alpha >\frac{6}{7}$.     

Dispersive shock waves in three dimensional Benjamin–Ono equation

Dispersive shock waves (DSWs) in the three dimensional Benjamin–Ono (3DBO) equation are studied with step-like initial condition along a paraboloid front. By using a similarity reduction, the problem of studying DSWs in three space one time (3+1) dimensions reduces to finding DSW solution of a (1+1) dimensional equation. By using a special ansatz, the 3DBO equation exactly reduces to the spherical Benjamin–Ono (sBO) equation. Whitham modulation equations are derived which describes DSW evolution in the sBO equation by using a perturbation method. These equations are written in terms of appropriate Riemann type variables to obtain the sBO-Whitham system. DSW solution which is obtained from the numerical solutions of the Whitham system and the direct numerical solution of the sBO equation are compared. In this comparison, a good agreement is found between these solutions. Also, some physical qualitative results about DSWs in sBO equation are presented. It is concluded that DSW solutions in the reduced sBO equation provide some information about DSW behavior along the paraboloid fronts in the 3DBO equation.     

Benjamin Ono方程的一些解析解

采用一种新型方法获得了Benjamin Ono方程的一些精确解析解，该方法的关键是使用齐次平衡思想和规则地混合指数函数构建试探解。对Benjamln方程，这种方法也被证明是有效的。     

A Sharp Bilinear Estimate for the Bourgain-Type Space with Application to the Benjamin Equation

This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/ill-posedness of the Cauchy problem for the Benjamin equation.     

Meshless formulation to two-dimensional nonlinear problem of generalized Benjamin–Bona–Mahony–Burgers through singular boundary method: Analysis of stability and convergence

In this study, the singular boundary method (SBM) is employed for the simulation of nonlinear generalized Benjamin–Bona–Mahony–Burgers problem with initial and Dirichlet-type boundary conditions. The θ-weighted finite difference method is used to discretize the time derivatives. Then the original equations are split into a system of partial differential equations. A splitting scheme is applied to split the solution of the inhomogeneous governing equation into homogeneous solution and particular solution. To solve this system, the method of particular solution (MPS) in combination with the SBM is used where the SBM is used for homogeneous solution and MPS is used for particular solution. Furthermore, the stability and convergence of the proposed method is conducted. Finally, several numerical examples with different domains are provided and compared with the exact analytical solutions to show the accuracy and efficiency in comparison with existing other methods.