[...]... Instability, and Higher Order Dispersion 511 15.1 The Near -Linear Case, 512 15.2 Characteristic Form of the Equations, 513 More Dependent Variables, 517 15.3 Type of the Equations and Stability, 517 15.4 Nonlinear Group Velocity, Group Splitting, Shocks, 519 15.5 Higher Order Dispersive Effects, 522 15.6 Fourier Analysis and Nonlinear Interactions, 527 16 Applications of the Nonlinear Theory NONLINEAR OPTICS,... which are basic to the understanding of waves t be covered But one could then fill volumes with solutions and iques for specific problems This is not the purpose of the book, hough the basic material on linear waves is included, some previous "rience with linear theory is assumed and the emphasis is on the ceptually more difficult nonlinear theory The study of nonlinear waves over a hundred years ago... ideas are presented in general, and topics for application or motivation are chosen with a general reader in mind It is assumed that flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, ocean waves from storms, and so on, are of universal interest Other fields are not excluded, and detailed discussion is given, for example, of nonlinear optics and waves in various mechanical... new phenomenon of the nonlinear theory is the appearance of shock waves, which are abrupt jumps in pressure, density, and velocity: the blast waves of explosions and the sonic booms of high speed aircraft But the whole intricate machinery of nonlinear hyperbolic equations had to be developed for their prediction, and a full understanding required analysis of the viscous effects and some aspects of kinetic... the main concepts for nonlinear hyperbolic waves We follow the ideas which were developed first in gas dynamics, but now we develop them in the simpler mathematical context The main nonlinear feature is the breaking of waves into shock waves, and the corresponding mathematical theory is the theory of characteristics and the special treatment of shock waves This Sec 1.2 HYPERBOLIC WAVES 7 is all presented... HYPERBOLIC WAVES 7 is all presented in detail in Chapter 2 The theory is then applied and supplemented in Chapter 3 in a full discussion of the topics of flood waves and similar waves noted earlier The first order equation (1.12) is called quasi -linear in that it is nonlinear in < but is linear in the derivatives . Whitham, Gerald Beresford, 1927- Linear and nonlinear waves. (Pure and applied mathematics) "A Wiley-Interscience publication." Bibliography: p. 1. Wave-motion, Theory of. 2. Waves. . LINEAR AND NONLINEAR WAVES G. B. WHITHAM F. R. S. Professor of Applied Mathematics California Institute of Technology A WILEY-INTERSCIENCE. Introduction and General Outline 1.1 1.2 1.3 1.4 PARTI HYPERBOLIC WAVES 2 Waves and First Order Equations 1 19 The Two Main Classes of Wave Motion, 2 Hyperbolic Waves, 4 Dispersive Waves, 9 Nonlinear