Titlebook: Singular Limits of Dispersive Waves; N. M. Ercolani,I. R. Gabitov,D. Serre Book 1994 Springer Science+Business Media New York 1994 asympto

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,KdV Equation With Nontrivial Boundary Conditions at , → ±∞,Let us consider KdV equation.with initial condition ., 0), which is a smooth function of ., rapidly (for simplicity - in the sense of Shwartz class) approaching two different limits as . → ±∞:

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Critical and Subcritical Cases of the Toda Shock Problem,In this paper we consider the Toda lattice of interacting particles. Physically, this is a one-dimensional lattice of particles interacting with exponential forces,

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978-1-4613-6054-4Springer Science+Business Media New York 1994

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Singular Limits of Dispersive Waves978-1-4615-2474-8Series ISSN 0258-1221

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On the Integrability of the Averaged KdV and Benney Equations,s (see [2], [4], [13], [20], [32]), for example the Whitham equations (the averaged 1-phase KdV equation):.(here ..=(..-..)/(..-..)); .(.), .(.) are the complete ellipticintegrals and Benney equations:

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Explicit Construction of The Lax-Levermore Minimizer for the KdV Zero Dispersion Limit, has constructed the global solution of the Whitham equations which matches at the phase transition boundaries to the characteristic solution of the inviscid Burgers’ equation for the given initial data.

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The Behavior of Solutions of the NLS Equation in the Semiclassical Limit,s. Numerical comparisons of the oscillations are made between the linear (“free”) and the cubic (defocusing and focusing) cases in one dimension. The integrability of the one-dimensional cubic NLS is exploited to give a complete global characterization of the weak limits of the oscillations in the defocusing case.

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A Numerical Study of Nearly Integrable Modulation Equations,er approximation to the perturbed flow in terms of modulated sine-Gordon wavetrains. Our goal here is to present . and to compare these predictions with the results of direct pde simulations using Ed Overman’s codes.