Efficient computation of steady solitary gravity waves

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as Tanaka’s method and Fenton’s high-order asymptotic expansion. Several important integral quantities are computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.     

A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation

In this paper, we employ the boundary-only meshfree method to find out numerical solution of the classical Boussinesq equation in one dimension. The proposed method in the current paper is a combination of boundary knot method and meshless analog equation method. The boundary knot technique is an integration free, boundary-only, meshless method which is used to avoid the known disadvantages of the method of fundamental solution. Also, we use the meshless analog equation method to replace the nonlinear governing equation with an equivalent nonhomogeneous linear equation. A predictor-corrector scheme is proposed to solve the resulted differential equation of the collocation. The numerical results and conclusions are obtained for both the ‘good’ and the ‘bad’ Boussinesq equations.     

Solitary deflection waves on the supersonic domain wall in yttrium orthoferrite

The moving antiferromagnetic vortices are accompanied by solitary deflection waves. These waves allow to investigate generation and nonlinear dynamics of the antiferromagnetic vortices on the moving domain wall with the help of the two- and three-fold digital high speed photography. On the quasi-relativistic domain wall the vortex dynamics is quasi-relativistic with the limiting velocity c=20 km/s, which is equal to the spin-wave velocity. The solitary deflection waves dynamics can be explained assuming existence of the gyroscopic force. A theory for the gyroscopic force in the orthoferrite domain wall is elaborating by A.K. Zvezdin et al. currently. We present a comparison of the theoretical and experimental results on the dynamics of the solitary deflection waves, which accompany the antiferromagnetic vortices in the domain wall of orthoferrites.     

Stability of solitary waves in nonlinear composite media

The system of equations for planar waves in elastic composite media in the presence of anisotropy is considered. In anisotropic case two two-parametric families of solitary waves are found in an explicit form. In case of the absence of anisotropy these two families coalesce into the unique three parametric family. The solitary wave solutions are found to be orbitally stable in a certain range of their phase speeds (range of stability) both in an anisotropic as well as in an isotropic materials. It is also shown that the initial value problem for the governing equations is locally well posed which is needed to prove the stability result. The local well-posedness of the initial value problem along with stability of solitary waves implies global existence result provided the initial data lie in a neighbourhood of a stable solitary wave. This complements the previous results of blow-up for this type of equations.     

Interfacial waves with free-surface boundary conditions: an approach via a model equation

In a two-fluid system where the lower fluid is bounded below by a rigid bottom and the upper fluid is bounded above by a free surface, two kinds of solitary waves can propagate along the interface and the free surface: classical solitary waves characterized by a solitary pulse or generalized solitary waves with nondecaying oscillations in their tails in addition to the solitary pulse. The classical solitary waves move faster than the generalized solitary waves. The origin of the nonlocal solitary waves can be understood from a physical point of view. The dispersion relation for the above system shows that short waves can propagate at the same speed as a “slow” solitary wave. The interaction between the solitary wave and the short waves creates a nonlocal solitary wave. In this paper, the interfacial-wave problem is reduced to a system of ordinary differential equations by using a classical perturbation method, which takes into consideration the possible resonance between short waves and “slow” solitary waves. In the past, classical Korteweg–de Vries type models have been derived but cannot deal with the resonance. All solutions of the new system of model equations, including classical as well as generalized solitary waves, are constructed. The domain of validity of the model is discussed as well. It is also shown that fronts connecting two conjugate states cannot occur for “fast” waves. For “slow” waves, fronts exist but they have ripples in their tails.     

略论胡适的留学教育观

对留学生在近代中国兴学运动中的作用,胡适提出了自己的看法.他从留学教育与国内教育、文化建设相结合的角度,阐述留学教育一定要以“为己国造新文明”为目的,“留学当以不留学为目的”,由此提出了“慎选留学”和“增设大学”的建议.胡适的观点有一定的积极意义.     

《新唐书·石国传》考辨

大宛都督府与原属贺鲁种落的千泉、俱兰、颉利三都督府及碎叶州,同置于显庆三年,但前者归安西都护府统辖,后四者属濛池都护府统辖;唐朝在石国置都督府,反映了石国在唐朝的西域统治体系中的重要地位;自隋大业年间以来,突厥人长期控制了石国;莫贺咄吐屯因功被册封为石王之事,应发生在开元二十八年;唐朝册封一个突厥吐屯为石国王,一方面说明唐朝长期利用突厥人控制塔什干地区;另一方面也说明突厥人长期控制着塔什干地区;石国至长安里程,《新唐书·石国传》少记1985～2005(唐)里;石国至周邻国家里程,《新唐书》之记也有错误。     

苏轼与齐文化

在源远流长的中国化史和风格各异的区域化系统中,对中国古代士人影响最深的莫过于齐鲁化。苏轼于古齐地为官,对齐化的积极学习、吸收及对齐化广泛传播的同时,齐化对苏轼也产生了重要影响。     

概念隐喻视角解读苏轼《水调歌头·明月几时有》

概念隐喻理论认为,隐喻是分属两个不同范畴或语义域之间的单项映射,通过源域与目标域之间的投射,完成语符表层到抽象实质的深层次转化。苏轼的《水调歌头·明月几时有》历来被称赞为咏月佳作,无数人为其思乡怀人的真挚情感所动容。除此之外,该篇字里行间也饱含苏轼对人生、世界等的哲思,概念隐喻理论将全面还原苏轼创作的原貌。     

微扰非线性薛定谔方程的孤子解

非线性薛定谔方程作为描述波包在弱非线性色散介质中传播的普遍方程。在光纤维中脉冲在皮秒范围内的传输可以用微扰非线性薛定谔方程来描述。文章采用实指数方法并借助Mathematica符号计算软件编程求其孤子解。