chapter Preface -- part 1 Part I: Nonlinear Dispersive Waves -- chapter 1 Numerical Simulations of Singular Solutions of the Nonlinear Schro¨dinger Equations, Xiao-Ping Wang -- chapter 2 Numerical Solution of the Nonlinear Helmholtz Equation, G. Fibich and S. Tsynkov -- chapter 3 Theory and Numerical Analysis of Boussinesq Systems: A Review / part 2 The Helmholtz Equation and Its Paraxial Approx- imations in Underwater Acoustics -- chapter 4 Finite Element Discretization of the Helmholtz Equation in an Underwater Acoustic Waveguide, D. A. Mitsoudis, N. A. Kampanis and V. A. Dougalis -- chapter 5 Parabolic Equation Techniques in Underwater Acoustics, D / chapter 6 Numerical Solution of the Parabolic Equation in Range–Dependent Waveguides / chapter 7 Exact Boundary Conditions for Acoustic PE Modeling Over an N2-Linear Half-Space, T. W. Dawson, G. H. Brooke and / part 3 Numerical Methods for Elastic Wave Propaga- tion -- chapter 8 Introduction and Orientation, P. Joly -- chapter 9 The Mathematical Model for Elastic Wave Propagation, P / chapter 10 Finite Element Methods with Continuous Displacement, P / chapter 11 Finite Element Methods with Discontinuous Displacement, P. Joly and C. Tsogka -- chapter 12 Fictitious Domains Methods for Wave Diffraction, P. Joly and C. Tsogka -- chapter 13 Space Time Mesh Refinement Methods, G. Derveaux, P. Joly and J. Rodr´ıguez -- chapter 14 Numerical Methods for Treating Unbounded Media, P. Joly and C. Tsogka -- part 4 Part IV: Waves in Compressible Flows -- chapter 15 High-Order Accurate Space Discretization Methods for Com- / chapter 16 Governing Equations, J. A. Ekaterinaris -- chapter 17 High-Order Finite-Difference Schemes, J. A. Ekaterinaris -- chapter 18 ENO and WENO Schemes, J. A. Ekaterinaris -- chapter 19 The Discontinuous Galerkin (DG) Method, J. A. Ekateri- naris.