静水槽孤立波的实验研究

本文在静水槽中复现出单孤立波,将实验得到的孤立波的波形和波速与理论值比较,极为接近。同时,考察了孤立波的碰撞行为,它表明了孤立波的粒子性。还验证了孤立波的非线性性质。     

非传播孤立波和表面张力

讨论关于表面张力的实验与理论分析之间的矛盾．把表面张力的能量当作高阶小量、导出了非传播孤立波的基本方程，得到的解与实验结果相符．     

非传播孤立波和表面张力

本文讨论了关于表面张力的实验与理论分析之间的矛盾把表面张力的能量当作高阶小量、导出了非传播孤立波的基本方程，得到的解与实验结果相符。     

孤立波与孤立子

简要阐述了孤立波与孤立子发现和研究的历史,并由此可看出力学基础研究的深刻意义.     

流体力学中的强迫孤立波

简要讨论了８０年代发现的以先驱孤立波和非传播孤立波为代表的流体力学中的强迫孤立波．介绍了这些孤立波产生的方法、力学模型、控制方程、研究现状及有待解决的问题．      

孤立波与多孔介质结构物的非线性相互作用

基于精确至Ｏ（εμ＾２,μ＾４）的多孔介质无压渗流模型方程和均匀流体质波动的Ｂｏｕｓｓｉｎｅｓｑ方程,本文对孤立波与多孔介质结构物的相互作用了较系统的数值实验。控制方程采用基于有限差分方程离散,在时域上采用了预估－校正方法进行了时间积分。在求解演化方程的过程中,引入“内迭代”过程实现流体域和多孔介质交界面的连接条件。结果表明孤立波在多孔介质上的反射与在不可渗透的界面上的反射类似,形成反向的孤立波但     

Whitham—Broer—Kaup浅水波方程新的多孤子解

Whitham-Broer-Kaup（简记WBK）方程具有重要的意义,至今人们只给出了它的单孤子解,本利用齐次平衡法并借助数学给出它新的多孤子解,并作为特例得到一类变式Boussinesq方程的多孤子解。     

微结构固体中钟型与扭结孤立波的演化

根据Mindlin理论和Murnaghan模型,首先建立了描述耗散、频散及非线性微结构固体中一维纵波传播的一种简单模型.然后利用有限差分方法,数值模拟了微结构效应对钟型与扭结孤立波演化的影响. 结果表明,随着微结构效应的减弱,钟型孤立波的幅度衰减以及非对称特征变得越来越明显;随着微结构效应的增强,扭结孤立波顶部出现的“帽子”状变化以及由此产生的非对称特征变得越来越明显.      

表面张力、黏性和驱动对非传播表面孤立波的影响

从理论上研究了表面张力、黏性和驱动对非传播表面孤立波的影响。指出表面张力使孤波高度增大、宽度减小．作出了孤波的等波响应曲线（ｅｑｕａｌ－ｗａｖｅ－ｒｅｓｐｏｎｓｅ－ｃｕｒｖｅｓ）并与实验结果进行了比较。     

Solitary waves and chaos in nonlinear visco-elastic rod

The dynamics behavior of a nonlinear visco-elastic rod subjected to axially periodic load is investigated theoretically and numerically. The weak longitudinal periodic load is distributed uniformly along the rod. Firstly, equation of motion of the rod is derived. Utilizing perturbation technique, we acquire Kdv type equation describing strain wave in the rod. By use traveling wave method, the elliptic cosine wave solution and the solitary wave solution in the rod are provided. Then, Melnikov method is applied to analyze the dynamic behaviour of the rod qualitatively. The explicit conditions for the onset of chaotic dynamics are yielded. With the help of the Poincare map method, phase trajectory and time-displacement history diagrams, the theoretical results obtained are checked.     

Solitary waves in stratified fluids and their interaction

A systematic procedure is proposed for obtaining solutions for solitary waves in stratified fluids. The stratification of the fluid is assumed to be exponential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direction of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be relied upon to provide the answers to the interaction problem.     

Solitary waves in longitudinally wrinkled and creased helicoids

Elastic ribbons subjected to twist and stretch handle multiple morphological instabilities, amongst others, the longitudinally wrinkled and creased helicoids are investigated in the present paper as promising periodic nonlinear waveguides. Modeling the ribbon by isogeometric Kirchhoff–Love shells, the first longitudinal buckling mode is recovered numerically and used into the Bloch–Floquet method to obtain dispersion curves. After analyzing the effects of the buckling pattern on the different wavemodes, it is shown that classical linear axial waves interact with bending ones and become dispersive. Additionally, as buckling involves geometrical nonlinearities, the structure is expected to host stable nonlinear waves. Indeed, clear supersonic rarefaction trains are observed experimentally and their characteristics are found in agreement with the weakly nonlinear Boussinesq model.     

Solitary waves in dissipative-dispersive systems with instability

The wave processes in a system described by a fourth-order partial differential equation with Burgers-Korteweg-de Vries nonlinearity are considered. The initial equation is reduced to a dynamical system of three equations, which is analyzed by means of a numerical method. It is shown that the equation for the waves in dissipative-dispersive systems with instability has solutions in the form of solitary waves and wave fronts.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 99–104, March–April, 1989.     

Solitary waves in a peridynamic elastic solid

The propagation of large amplitude nonlinear waves in a peridynamic solid is analyzed. With an elastic material model that hardens in compression, sufficiently large wave pulses propagate as solitary waves whose velocity can far exceed the linear wave speed. In spite of their large velocity and amplitude, these waves leave the material they pass through with no net change in velocity and stress. They are nondissipative and nondispersive, and they travel unchanged over large distances. An approximate solution for solitary waves is derived that reproduces the main features of these waves observed in computational simulations. It is demonstrated by numerical studies that the waves interact only weakly with each other when they collide. Wavetrains composed of many non-interacting solitary waves are found to form and propagate under certain boundary and initial conditions.     

Solitary stokes waves in heavy-fluid slit flow

Flow with a solitary Stokes wave is obtained as a result of solving the plane nonlinear problem of the steady flow of an ideal heavy incompressible fluid into a slit at the bottom of a vessel for a narrow range of Froude numbers on which there exists a solution with a jet surface descending monotonically to the slit [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 173–176, November–December, 1991.The authors are grateful to A. N. Ivanov and G. Yu. Stepanov for their assistance and useful discussions.     

Solitary waves and conjugate flows in a three-layer fluid

Interfacial symmetric solitary waves propagating horizontally in a three-layer fluid with constant density of each layer are investigated. A fully nonlinear numerical scheme based on integral equations is presented. The method allows for steep and overhanging waves. Equations for three-layer conjugate flows and integral properties like mass, momentum and kinetic energy are derived in parallel. In three-layer fluids the wave amplitude becomes larger than in corresponding two-layer fluids where the thickness of a pycnocline is neglected, while the opposite is true for the propagation velocity. Waves of limiting form are particularly investigated. Extreme overhanging solitary waves of elevation are found in three-layer fluids with large density differences and a thick upper layer. Surprisingly we find that the limiting waves of depression are always broad and flat, satisfying the conjugate flow equations. Mode-two waves, obtained with a periodic version of the numerical method, are accompanied by a train of small mode-one waves. Large amplitude mode-two waves, obtained with the full method, are close to one of the conjugate flow solutions.     

Short-wave asymptotics for weak shock waves and solitons in mechanics

Some recent applications of the theory of non-linear waves in smoothly inhomogeneous and weakly dissipative media are discussed in the paper. The possibilities of “linear-ray” approximation when the non-linear self-refraction effects may be neglected in comparison with the non-linear wave distortion along the rays are demonstrated for weak acoustic shocks in stratified atmospheres and ocean, the solitary waves in shallow water of variable depth and the solitons in elastic rods.