Alexandr A. Lokshin, Elena A. Sagomonyan

Nonlinear Waves in Inhomogeneous and Hereditary Media

• Broschiertes Buch

Produktbeschreibung

This monograph presents the study of one-dimensional waves

in inhomogeneous and hereditary media (i.e., media with

memory). A new mathematically rigorous factorization method

is applied which yields either an exact or an asymptotic

decomposition of the nonlinear wave equations under

consideration into first order multipliers.

A central result presented in the book is a factorization

theorem for the simple wave equation with constant

coefficients. It permits to view Riemann invariants and

simple waves from a different angle and is used to go over

to wave equations with variable coefficients and memory.

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Dieser Band liefert eine Studie über eindimensionale Wellen in inhomogenen und hereditaren Medien (d.h. Medien mit "Gedächtnis"). Die Autoren wenden eine neue, mathematisch exakte Faktorisierungsmethode an, die entweder zur exakten oder zur asymptotischen Zerlegung nichtlinearer Wellengleichungen in Multiplikatoren erster Ordnung führt.

Produktdetails

• Research Reports in Physics
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-54536-1
• 1992
• Seitenzahl: 140
• Erscheinungstermin: 30. März 1992
• Englisch
• Abmessung: 235mm x 155mm x 8mm
• Gewicht: 200g
• ISBN-13: 9783540545361
• ISBN-10: 3540545360
• Artikelnr.: 29006509

Inhaltsangabe

1. Nonlinear Waves in Homogeneous Media.- 1.1 Preliminaries.- 1.2 Nonlinear Hyperbolic Equations of the First Order.- 1.3 Exact Factorization of the Nonlinear Wave Equation with Constant Coefficients.- 1.4 Shock-Wave in a Simple System.- 1.5 The Shock-Wave in a Simple System (Continuation).- 2. Nonlinear Short Waves of Finite Amplitude in Inhomogeneous Media.- 2.1 Asymptotic Factorization of the Nonlinear Wave Equation with a Variable Coefficient.- 2.2 When is the Factorization Exact?.- 2.3 Asymptotic Factorization of the General Nonlinear Wave Equation with Variable Coefficients.- 2.4 Evolution of Maximal Amplitude of the Stress Wave.- 2.5 Propagation of a Stress Wave in a Homogeneous Nonlinear Elastic Rod Located in the Gravity Field.- 3. Nonlinear Waves in Media with Memory.- 3.1 Hereditary Elasticity.- 3.2 Small Quadratic Nonlinearity.- 3.3 Continuous Stationary Profile Waves and Nonzero Solutions of Homogeneous Integral Volterra Equations.- 3.4 Stationary Profile Shock-Waves and Self-Coordinated Integral Volterra Equations.- 3.5 Waves Tending to a Stationary Profile.- 3.6 Nonstationary Waves Analog of the Landau-Whitham Formula.- 3.7 General Nonlinearity. Further Factorization Theorems for Nonlinear Wave Equations with Memory.- 3.8 Nonstationary Waves for an Exponential Memory Function.- 3.9 Reflection of a Wave from the Boundary Between Linear Elastic and Nonlinear Hereditary Media.- 3.10 The Exactly Factorizable Linear Wave Equation with Memory and a Variable Coefficient.- References.