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Saturday, May 16, 2020 | History

4 edition of Nonlinear waves in inhomogeneous and hereditary media found in the catalog.

Nonlinear waves in inhomogeneous and hereditary media

by A. A. Lokshin

  • 313 Want to read
  • 37 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Wave-motion, Theory of.,
  • Deformations (Mechanics),
  • Elastic solids.

  • Edition Notes

    StatementA.A. Lokshin, E.A. Sagomonyan.
    SeriesResearch reports in physics, Nonlinear dynamics, Springer series in nonlinear dynamics.
    ContributionsSagomoni͡a︡n, E. A.
    Classifications
    LC ClassificationsQA935 .L8713 1992
    The Physical Object
    Paginationx, 121 p. :
    Number of Pages121
    ID Numbers
    Open LibraryOL1703335M
    ISBN 103540545360, 0387545360
    LC Control Number92004434

    Solitons are nonlinear waves. As a preliminary definition, a soliton is considered as solitary, traveling wave pulse solution of nonlinear partial differential equation (PDE). The nonlinearity will play a significant role. For most dispersive evolution equations these solitary waves would scatter inelastically and lose 'energy' due to the radiation.   G.B. Whitham Linear and Nonlinear Waves John Wiley & Sons Inc. Acrobat 7 Pdf Mb. Scanned by artmisa using Canon DRC + flatbed.

    In the left hand side of Eq. (), we find the part of the homogeneous wave equation for propagation of electromagnetic waves in vacuum, while the right hand side described the modifications to the vacuum propagation due to the interaction between light and matterIn this respect, it is now clear that the electric polarisation effectively acts as a source term in the mathematical description of. nonlinear waves can be traced back to the key papers of Boussinesq in the ’s, the field has experienced tremendous growth in past 30 years. Some of the growth was stimulated by T. B. Benjamin’s publication “The sta-bility of solitary waves” whose treatment of the Korteweq-de Vries equation.

    7{The Nonlinear Wave Equation and the Interaction of Waves MATH 22C 1. Introduction Just as the nonlinear advection equation looks the same as the linear advection equation ut+ cux = 0 except that the speed of sound cdepends on the solution u, so also the nonlinear wave equation is the linear wave equation utt c2uxx = 0 under the assumption File Size: KB. It is possible to obtain nonlinear solutions for waves on shear flows for special cases of the vorticity distribution. For waves on a constant shear flow, Kishida and Sobey (), calculated a third-order so-lution, while Dalrymple (), used a numerical method. It is conceivable that in future such solutions will become more Size: KB.


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Nonlinear waves in inhomogeneous and hereditary media by A. A. Lokshin Download PDF EPUB FB2

Nonlinear Waves in Inhomogeneous and Hereditary Media. Authors: Lokshin, Alexandr A., Sagomonyan, Elena A.

Nonlinear Waves in Media with Memory.- Hereditary Elasticity.- Linear Equations.- Nonlinear Equations.- Small Quadratic Nonlinearity.- Asymptotic Factorization of the Nonlinear Wave Equation with Memory.- Why Can't the Factorization be Exact?.- Single-Wave Equation.- Condition on the Shock for the.

Nonlinear Waves in Inhomogeneous and Hereditary Media. Series: Research Reports in PhysicsCited by: 4. Int. ^on-Linear Mechanics. Vol. t, pp. /89 S+ Printed in Great Britain.

Pcrgamon Press pic PROPAGATION OF NON-LINEAR WAVES IN INHOMOGENEOUS HEREDITARY MEDIA A. RAVASOO Department of Mechanics, Institute of Cybernetics of the Estonian Academy of Sciences, Akadeemia by: 2.

It may be noted that nonlinear waves get modified in an essential way in an inhomogeneous plasma. For instance, the amplitude, width, and propagation velocity of an ion-acoustic solitary wave will change as the latter moves in an inhomogeneous plasma (Nishikawa and Kaw [], John and Saxena [], Rao and Varma [], Shivamoggi [, Author: Bhimsen K.

Shivamoggi. Whitham's book on linear (e.g., sine waves) and nonlinear (e.g., solitons and shocks) waves is a very thorough and well written narrative of the various manifestations of the fluctuations we call waves. Whether a beginning graduate student or researcher, the book provides very insightful and useful derivations combined with physically Cited by: In a number of physical problems, one deals with evolution of envelopes of high-frequency waves in inhomogeneous nonlinear media (see Ref.

1 and references therein). Of special interest is the situation when the wave is passing from a focussing domain into a defocussing one, or vice : Boris A.

Malomed. waves on the ocean, sound waves in the air or other media, and electromagnetic waves, of which visible light is a special case. A common feature of these examples is that they all can be described by partial differential equations (PDE). The purpose of these lecture notes is to give an introduction to various kinds of PDE describing Size: 1MB.

In the inhomogeneous material, the wave characteristics sensitivity to various material properties variations is also different. The variation of the first harmonic amplitude and the phase shift and the second harmonic phase shift is strongly sensitive to the density and linear elastic coefficient variation but less sensitive to the nonlinear elastic coefficient by: Nonlinear Maxwell Equations in Inhomogeneous Media We allow ε(r) to be Hermitian with complex entries, rather than simply real symmetric, since such permittivity tensors occur for a general dielectric (gyrotropic) media (see, for instance, [16] p and [29], p.

49). We also allow for PNL (E)a general analytic dependence in E(), PNL (E. S.B. Lebles book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification.

The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations.

Nonlinear Waves. The study of Nonlinear Wave Phenomena is of broad scientific interest. It pertains to the understanding of real water waves, the interaction of light with matter, optical fiber transmission, traffic flow, earthquakes and galaxy formation. As a modern mathematical discipline nonlinear wave theory frequently explores asymptotic.

Nonlinear acoustics (NLA) is a branch of physics and acoustics dealing with sound waves of sufficiently large amplitudes. Large amplitudes require using full systems of governing equations of fluid dynamics (for sound waves in liquids and gases) and elasticity (for sound waves in solids).

These equations are generally nonlinear, and their traditional linearization is no longer possible. Nonlinear Waves And Shocks By Cathleen S. Morawetz Lectures delivered at the Indian Institute of Science, Bangalore under the T.I.F.R.

— Programme In Applications of Mathematics Notes by P.S. Datti Published for the Tata Institute of Fundamental Research, Bombay Springer–Verlag Berline-Heidelberg–New York The first and second international conferences: “Nonlinear Waves Theory and Applications” took place in Beijing, China in the summers of and These conferences were characterized by their high level of scientific content and attractive venue for collegial interactions.

Hereditary Colorectal. Hereditary Colorectal Cancer By M.a. Rodriguez-bigas English Hardcover Book Fr. $ This graduate-level course provides a unified treatment of nonlinear oscillations and wave phenomena with applications to mechanical, optical, geophysical, fluid, electrical and.

Title: Global solutions of nonlinear wave equations in time dependent inhomogeneous media. Authors: Shiwu Yang (Submitted on 21 Octlast revised 26 Apr (this version, v4))Cited by: 2. WAVES IN NONLINEAR ELASTIC MEDIA WITH INHOMOGENEOUS PRE-STRESS A thesis submitted to the University of Manchester for the degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences Tom Shearer School of Mathematics.

DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves.

References. Index. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media.

The examples used come mainly from gas dynamics, water waves and viscoelastic waves. this book readwhy 6.Fenton, J.D. () Numerical Methods for Nonlinear Waves, in Advances in Coastal and Ocean Engineering, Vol.

5, ed. P.L.-F. Liu, pp, World Scientific: Singapore. Numerical methods for nonlinear waves John D. Fenton Department of Civil and Environmental Engineering, The University of Cited by: Motivated by the propagation of nonlinear sound waves through relaxing hereditary media, we study a nonlocal third-order Jordan-Moore-Gibson-Thompson acoustic wave equation.