Title | Selected Topics in Nonlinear Wave Mechanics [electronic resource] / edited by C. I. Christov, A. Guran |
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Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0095-6 |
Descript | XIII, 263 p. online resource |
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