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Selected Topics in Nonlinear Wave Mechanics (2002)

Christov, C. I. [editor.] ; Guran, A. [editor.] ; SpringerLink 〈Online service〉

Boston, MA :Birkhäuser Boston :

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UID:

almahu_9947362879702882

Umfang: XIII, 263 p. , online resource.

ISBN: 9781461200956

Inhalt: This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

Anmerkung: 1 Elastic Surface Waves, Resonances, and Inverse Acoustic Scattering -- 1.1 Introduction -- 1.2 Waves on elastic plates: Lamb-type and Scholte-Stoneley waves -- 1.3 Acoustic Interactions Wich Ocean-Floor Sediments -- 1.4 Conclusions -- 2 Amplitude Equation Models for the Interaction of Shocks with Nonlinear Dispersive Wave Envelopes -- 2.1 Introduction -- 2.2 The Weak Coupling Limit -- 2.3 The Riemann Problem -- 2.4 The Zero Diffusion Limit -- 2.5 Dynamics Prior to Shock Onset -- 2.6 The Incompressible Limit -- 2.7 Exact Solutions -- 2.8 The ? = 0 Problem -- 2.9 The Multi-Scale Expansions -- 2.10 Modulation Equations for the Dispersive Wave -- 2.11 Analysis of the Effective Shock Equation for the Nonlinear Limit -- 2.12 Analysis of the Effective Shock Equation in the Linear Limit -- 2.13 Numerical Experiments -- 3 Some Aspects of One-Dimensional Finite Amplitude Elastic Wave Propagation -- 3.1 First Order Equations -- 3.2 Systems of First Order Equations -- 3.3 Elastic Strings -- 3.4 Problems for membranes -- 3.5 Some problems for three dimensional elastic bodies -- 3.6 Thermodynamic considerations -- 4 Nonlinear Duality Between Elastic Waves and Quasi-particles -- 4.1 Introduction -- 4.2 Hyperbolicity and Conservation Laws -- 4.3 Elasticity as a field theory -- 4.4 Solitonic systems -- 4.5 Nearly integrable systems -- 4.6 Examples from Continuum Mechanics -- 4.7 Conclusions -- 5 Time-Harmonic Waves in Pre-Stressed Dissipative Materials -- 5.1 Introduction -- 5.2 Linearized Equations in Solids -- 5.3 Constitutive Equation for Solids -- 5.4 Linearized Equations and Restrictions for Fluids -- 5.5 Propagation Condition for Inhomogeneous Waves -- 5.6 Dissipation and Wave Decay -- 5.7 A New Approach to Wave Propagation -- 5.8 Rays in Pre-Stressed Solids -- 6 Dissipative Effects on the Evolution of Internal Solitary Waves in a t Sheared, Stably Stratified Fluid Layer -- 6.1 Introduction -- 6.2 Model system -- 6.3 Discussion -- 6.4 Conclusions -- 7 Dissipative Nonlinear Strain Waves in Solids -- 7.1 Introduction -- 7.2 Modelling of nonlinear waves in an elastic rod -- 7.3 Mathematical tools for analysis of the governing equations -- 7.4 Amplification of a strain solitary wave in a narrowing rod -- 7.5 Selection of nonlinear strain waves in an elastic rod due to the influence of an external medium -- 7.6 Influence of macro- and micro-dissipation on the formation of dissipative solitary waves -- 7.7 Concluding remarks.

In: Springer eBooks

Weitere Ausg.: Printed edition: ISBN 9781461266099

Sprache: Englisch

DOI: 10.1007/978-1-4612-0095-6

URL: http://dx.doi.org/10.1007/978-1-4612-0095-6

URL: Volltext

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Selected topics in nonlinear wave mechanics (2002)

Temelski, Christo 1948- ; Guran, Ardéshir 1959- ; Christov, Christo I. [Hrsg.] 1951-

Boston [u.a.] : Birkhäuser | New York : Springer Science+Business Media

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UID:

gbv_346377889

Umfang: XII, 263 S , Ill., graph. Darst , 24 cm

ISBN: 0817640592 , 3764340592 , 9781461266099

Anmerkung: Includes bibliographical references and index

Weitere Ausg.: Erscheint auch als Online-Ausgabe Christov, Christo I., 1951 - Selected Topics in Nonlinear Wave Mechanics Boston, MA : Birkhäuser, 2002 ISBN 9781461200956

Sprache: Englisch

Fachgebiete: Physik , Mathematik

RVK:

SK 950

RVK:

UF 6200

RVK:

UF 5000

Schlagwort(e): Nichtlineare Wellengleichung ; Nichtlineare Welle ; Nichtlineare Wellenausbreitung ; Elastische Welle ; Wellenmechanik ; Aufsatzsammlung

URL: Inhaltstext

Mehr zum Autor: Guran, Ardéshir 1959-

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Online-Ressource

Selected Topics in Nonlinear Wave Mechanics (2002)

Christov, Christo I. 1951- ; Guran, A. [Hrsg.]

Boston, MA : Birkhäuser

zur Merkliste hinzufügen auf der Merkliste

Details

UID:

gbv_1655012134

Umfang: Online-Ressource (XIII, 263 p, online resource)

ISBN: 9781461200956

Serie: SpringerLink

Inhalt: This comprehensive reference text gives an overview of the current state of nonlinear wave mechanics in both elastic and fluid media. Consisting of self-contained chapters, the book covers new aspects on strong discontinuities (shock waves) and localized self- preserving (permanent) shapes (solitary waves and solitons). Special attention is devoted to the kinematics and dynamics of permanent waves when dissipative effects are added to the original balance between nonlinearity and dispersion. Key features include: * survey chapters written in an accessible style by leading specialists * coverage of emerging topics in the field * interdisciplinary approach integrating mathematical theory and physical applications of nonlinear waves in elastic and fluid media * treatment of the intrinsic mechanisms of propagation of different types of nonlinear waves * presentation of analytical methods for solving wave propagation problems in elastic and fluid media * user-friendly index 'Selected Topics in Nonlinear Wave Mechanics' provides readers with recent developments in the nonlinear propagation and scattering of waves in both elastic solids and liquids. The book is useful for applied mathematicians, physicists, mechanical, civil and aerospace engineers, as well as graduate students in those fields. Contributors: R.M. Axel, C.I. Christov, A. Guran, J.B. Haddow, G.A. Maugin, A. Morro, A. Nagl, P.K. Newton, A.V. Porubov, R.J. Tait, H. sberall, M.G. Velarde, W.B. Zimmerman

Weitere Ausg.: ISBN 9781461266099

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Selected topics in nonlinear wave mechanics Boston [u.a.] : Birkhäuser, 2002 ISBN 0817640592

Weitere Ausg.: ISBN 3764340592

Weitere Ausg.: ISBN 9781461266099

Sprache: Englisch

Fachgebiete: Physik , Mathematik

RVK:

UF 5000

RVK:

SK 950

Schlagwort(e): Nichtlineare Wellenausbreitung

DOI: 10.1007/978-1-4612-0095-6

URL: Volltext (lizenzpflichtig)

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