3 edition of **On non-linear dispersive water waves.** found in the catalog.

On non-linear dispersive water waves.

Hendrik Willem Hoogstraten

- 136 Want to read
- 29 Currently reading

Published
**1969**
by Waltman in Delft
.

Written in English

- Water waves.,
- Differential equations, Partial.,
- Nonlinear waves.

Classifications | |
---|---|

LC Classifications | QA927 .H67 |

The Physical Object | |

Pagination | 84 p. |

Number of Pages | 84 |

ID Numbers | |

Open Library | OL4359047M |

LC Control Number | 78406137 |

In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase waves, in this context, are waves propagating on the water surface, with gravity and surface tension as the restoring a result, water with a free surface is generally considered to be a dispersive medium. the!is complex valued and the wave solution decays exponential in time. On the other hand the transport equation ut ux = 0 and the one dimensional wave equation utt = uxx have traveling waves with constant velocity. 2In this light the linear wave equation in dimension higher than two is dispersive as the solution is supported on the cone ˝= j˘ Size: KB.

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit Price: $ dispersive wave equations" Sergey Dyachenko, Katelyn Leisman, Denis Silantyev: "Nonlinear waves in optics, luids and plasma" Michael Sigal, Jianfeng Lu: "Mathematical perspectives in quantum mechanics and quantum chemistry" Alexander O. Korotkevich and Pavel Lushnikov: "Nonlinear waves, singularities,vortices, and turbulence inFile Size: 1MB.

The theory for the non-linear dispersion of periodic waves in uniform depth is well established [see Whitham () for a review] and has been used to heuristically correct wave phase speeds in linear refraction models (Dingemans , and references therein). Nonlinear dispersion effects on random waves in shallow water are less well un-derstood. Linear water waves A one-dimensional linear wave can be represented by Fourier components u = ℜ{Aexp(ikx −iωt)}, (1) where k is the wavenumber, ω is the frequency, and A is the amplitude. Both ω and A may be functions of k. The linear wave dynamics are determined by the dispersion relation ω = ω(k), (2) the form of which depends on.

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It is a basic book for graduate students and researchers in fluidoynamics. Linear, nonlinear dispersive and shock dispersionless waves in are described in detail in gas dynamics and water waves. A short review of the soliton theory is by: 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.

Throughout the twentieth century, development of the linearized theory of wave motion in fluids and hydrodynamic stability has been steady and significant.

In the last three decades there have been remarkable developments in nonlinear dispersive waves in general, nonlinear water waves in particular, and nonlinear instability Edition: 1.

Book description The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth by: 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 Edition: 1. About this book Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared indue to the increased use of nonlinear waves.

It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves.

Typical examples include the vibrations of a string, propagation of electromagnetic waves, waves on the surface of water and so on. Again such systems may be classified into linear and nonlinear : M. Lakshmanan, S.

Rajasekar. The slow dispersion of non-linear water waves is studied by the general theory developed in an earlier paper (Whitham b). The average Lagrangian is calculated from the Stokes expansion for periodic wave trains in water of arbitrary depth.

This Lagrangian can be used for the various applications described in the above reference. This study investigates the phenomena of evolution of two-dimensional, fully nonlinear, fully dispersive, incompressible and irrotational waves in water of uniform depth in single and in double layers.

The study is based on an exact fully nonlinear and fully dispersive (FNFD) wave model developed by Wu (, a). This FNFD wave model is first based on two exact equations involving three Cited by: 2.

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg-de Vries (KdV) in the nineteenth century. In the s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those Cited by: This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves.

Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and : Birkhäuser Basel. Genre/Form: Academic theses: Additional Physical Format: Online version: Hoogstraten, Hendrik Willem.

On non-linear dispersive water waves. Delft, Waltman []. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values.

at the NSF-CBMS regional conference on nonlinear and dispersive wave equations at New Mexico State University, held in June Its objective is to present some aspects of the global existence theory (and in particular, the regularity and scattering theory) for various nonlinear dispersive and wave equations, such as the.

This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena.

Method of multiple scales: Linear and nonlinear pendulum 86 Exercises 96 5 Water waves and KdV-type equations 98 Euler and water wave equations 99 Linear waves Non-dimensionalization Shallow-water theory Solitary wave solutions Exercises 6 Nonlinear Schrodinger models and water waves¨ File Size: 3MB.

Nonlinear Dispersive Waves by Mark J. Ablowitz,available at Book Depository with free delivery worldwide.5/5(1). The NLSE is one of the basic mathematical models describing nonlinear dispersive wave interactions in a number of natural and engineering systems 6, 7.

Simulation of nonlinear free surface dispersive water waves Article in Journal of Hydro-environment Research 1(2) December with 53 Reads How we measure 'reads'.

Simulation of the nonlinear shallow water waves is essential for studying the interaction of such waves with marine structures. In the deep water region, the nonlinearity play a major role when the extreme wave interacts with the offshore structures, where as in the near shore, due to the change in bathymetry, the nonlinearity play a major role Cited by: 4.Create a new account.

Are you an ASCE Member? We recommend that you register using the same email address you use to maintain your ASCE Member account.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.