Linear and Nonlinear Waves
Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due 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. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.
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Introduction and General Outline
Waves and First Order Equations
28 other sections not shown
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amplitude appropriate approximation argument asymptotic axis behavior boundary conditions Chapter characteristic equations characteristic form characteristic velocities coefficients conservation equation consider constant corresponding curve density dependence derivatives detail determined differential equations dimensional discontinuity discussion dispersion relation dispersive waves disturbance eikonal equation energy exact solution example expansion expression finite flow fluid formulation Fourier frequency function gas dynamics geometrical geometrical optics given group velocity heat equation Hence higher order hyperbolic initial conditions initial value problem integral interaction introduce kinematic wave Klein-Gordon equation Korteweg-deVries equation Lagrangian Laplace's equation linear theory near-linear nonuniform normal noted obtained parameter perturbation phase plane propagation quantities ray tube region satisfy Section shock conditions shock structure shock-shock shown in Fig simple wave Sine-Gordon equation solitary waves solved speed surface tion transformation typical uniform variables variational principle vector water waves wave equation wave number wavefront written zero