NONLINEAR DISPERSIVE WAVE PHENOMENA 1. Introduction The study of nonlinear dispersive wave equations is a central field in the area of nonlinear partial differential equations (p.d.e.’s). The fundamental discoveries and the understanding of the properties of solitary wave solutions for the Korteweg-de Vries
discussed in the general context of nonlinear dispersive waves by Benney and Newell (1967) (see also Ostrows-kii 1967). For water waves it was ﬁrst derived by Zak-harov (1968) using a spectral method and by Hasimoto and Ono (1972) and Davey (1972) using multiple-scale methods. The nonlinear Schro¨dinger equation in one- The structural stability of waves of large amplitude is investigated using the approach presented earlier in the literature. Multiscaled waves without vortex core are shown to be structurally unstable. It is anticipated that complicated multiscaling phenomena could exist for solitary waves in various geophysical situations. NONLINEAR DISPERSIVE WAVES 169 The arbitrary parameter x0 gives the location of the point of maximum amplitude of the solitary wave at time t = 0. These solitary waves propagate without change of form at the steady speed (1 + @U), determined by their maximum amplitude U. Abstract Large amplitude Alfvén waves are frequently found in magnetized space and laboratory plasmas. Our objective here is to discuss the linear and nonlinear properties of dispersive Alfvén waves (DAWs) in a uniform magnetoplasma.
6. Phase Shift Modulations for Perturbed Strongly Nonlinear Oscillatory Dispersive Waves. 7. On the Zakharov-Schulman Equations. 8. Hamiltonian Long-Wave Approximations for Water Waves in a Uniform Channel. 9. A Sub-Centre Manifold Description of the Evolution and Interaction of Nonlinear Dispersive Waves. 10. The three-dimensional (3-D) nonlinear and dispersive PDEs system for surface waves propagating at undisturbed water surface under the gravity force and surface tension effects are studied. By applying the reductive perturbation method, we derive the equation, the semilinear wave equation, the Korteweg-de Vries equation, and the wave maps equation. These four equations are of course only a very small sample of the nonlinear dispersive equations studied in the literature, but they are reasonably representative in that they showcase many of the techniques used for more general
NONLINEAR DISPERSIVE WAVES ON TREES JERRY L. BONA AND RADU C. CASCAVAL ABSTRACT. We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Speci cally, westudytheBenjamin-Bona-Mahony(BBM)equa- Sep 01, 2015 · Even more complicated behaviour of waves in solids is observed if nonlinear effects enter into the play [5,12]. The main attention is paid usually for travelling solitary wave solution of the corresponding nonlinear dispersive-dissipative Korteveg-de Vries-type equation [5,12-19]. Get this from a library! Nonlinear dispersive waves : asymptotic analysis and solitons. [Mark J Ablowitz] -- "The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century.
Nonlinear Cherenkov Radiation in an Anomalous Dispersive Medium Huaijin Ren,1,2 Xuewei Deng,1,3,† Yuanlin Zheng,1,2 Ning An,1,2 and Xianfeng Chen1,2,* 1Department of Physics, Key Laboratory for Laser Plasmas (Ministry of Education) Shanghai Jiao Tong University, In this paper, we take advantage of the overlapping asymptotic regime that applies to both the NLS and Whitham modulation descriptions in order to develop a universal analytical description of dispersive shock waves (DSWs) generated in Riemann problems for a broad class of integrable and nonintegrable nonlinear dispersive equations.
Non-Linear Waves in Dispersive Media introduces the theory behind such topic as the gravitational waves on water surfaces. Some limiting cases of the theory, wherein proof of an asymptotic class is necessary and generated, are also provided. The first section of the book discusses the notion of linear approximation. Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions Thesis directed by Professor Mahmoud I. Hussein Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or uid ow are all likely to
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