Singular Limits of Dispersive Waves

Whitham Modulation Equations and Their Exact Solutions.- The Whitham Equation and Shocks in the Toda Lattice.- Semiclassical Behavior in the NLS Equation: Optical Shocks-Focusing Instabilities.- A Numerical Study of Nearly Integrable Modulation Equations.- The Quasiclassical Limit of the Inverse Scattering Method.- Solving Dispersionless Lax Equations.- Nonisospectral Symmetries of the KdV Equations and the Corresponding Symmetries of the Whitham Equations.- Breaking Problem in Dispersive Hydrodynamics.- Whitham Deformations of Two-Dimensional Lioville Tori.- Higher Rank Darboux Transformations.- On the Initial Value Problem of the Whitham Averaged System.- On the Integrability of the Averaged KdV and Benney Equations.- Explicit Construction of the Lax-Levermore Minimizer for the KdV Zero Dispersion Limit.- Dispersionless Limit of Integrable Systems in 2+1 Dimensions.- Asymptotics and Limits.- KdV Equation with Nontrivial Boundary Conditions at x ? ±?.- Long-time Asymptotics for the Autocorrelation Function of the Transverse Ising Chain at the Critical Magnetic Field.- Resonances in Multifrequency Averaging Theory.- Billiards Systems and the Transport Equation.- The Behavior of Solutions of the NLS Equation in the Semiclassical Limit.- Critical and Subcritical Cases of the Toda Shock Problem.- Existence and Regularity of Dispersive Waves.- Geometric Phases and Monodromy at Singularities.- Nonlinear Waves and the 1:1:2 Resonance.- Defects of One-Dimensional Vortex Lattices.- Oscillations Arising in Numerical Experiments.- On the Hierarchy of the Generalized KdV Equations.- A New Theory of Shock Dynamics.