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Surveys in Applied Mathematics is a series of volumes, each of which contains expo of several topics in mathematics and their applications. They are written at a sitions level accessible to advanced graduate students and interested nonspecialists, but they also contain the results of recent research. Volume I consists of three articles. The first is the classic paper of J. B. Keller and R. M. Lewis, "Asymptotic Methods for Partial Differential Equations: The Reduced Wave Equation and Maxwell's Equations." The second is by D. W. McLaughlin and E. A. Overman on "Whiskered Tori for Integrable Pde's: Chaotic Behavior in Near Integrable Pde's." This is a systematic analytical and numerical study of near integrable wave equations, including the sine-Gordon equations and the perturbed nonlinear SchrOdinger equation. The third article is by G. Papanicolaou on "Diffusion in Random Media." It is an introductory survey of homogenization methods for the diffusion equation with random diffusivity.
List of contents
1. Wave Front Propagation for KPP-Type Equations.- 1.1. Introduction.- 1.2. Wave Fronts in a Flow with Nontrivial Velocity Profile.- 1.3. Generalizations and Remarks.- 1.4. Wave Front Propagation in Anisotropic Media.- 1.5. Wave Front Propagation in a Tube with Absorbing Walls.- 1.6. Wave Front Propagation in Slowly Nonhomogeneous Media.- 1.7. RDE Systems of KPP Type.- 1.8. RDEs in Narrow Branching Channels.- References.- 2. Particle and Wave Transmission in One-Dimensional Disordered Systems.- 2.1. Introduction.- 2.2. Localization.- 2.3. Transmission Coefficient.- 2.4. Reflection and Resonances.- 2.5. Probability Distributions of Transmittivity Decrements for High Energies.- 2.6. Observable Transparency.- 2.7. Waves in the Randomly Stratified Medium.- 2.8. Disorder and Nonlinearity.- References.- 3. Asymptotic Equations for Nonlinear Hyperbolic Waves.- 3.1. Introduction.- 3.2. Hyperbolic Waves.- 3.3. Dissipation and Dispersion.- 3.4. Miscellaneous Applications.- 3.5. Diffraction.- 3.6. Other Topics.- References.
