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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Semiclassical Behavior in the NLS Equation: Optical Shocks - Focusing Instabilities, defocusing case, and verify it with numerical experiments. We also point out an application of that theory to the physical problem of optical shocking in fibers. Following that we consider the focusing case. We argue that the the failure of the existing theory is a result of the modulational instab

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A Numerical Study of Nearly Integrable Modulation Equations,nal attractors and bifurcation phenomena. These attractors are fully nonlinear (i.e., order one amplitude) space-time structures which have been independently measured (using the spectral transform) in terms of integrable, sine-Gordon modes. Based on these direct measurements, we posit a leading ord

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On the Integrability of the Averaged KdV and Benney Equations,al hamiltonian systems possessing a complete set of Riemann invariants arising in the theory of multiphase averaging of completely integrable equations (see [2], [4], [13], [20], [32]), for example the Whitham equations (the averaged 1-phase KdV equation):.(here ..=(..-..)/(..-..)); .(.), .(.) are t

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Explicit Construction of The Lax-Levermore Minimizer for the KdV Zero Dispersion Limit,veraged system of modulation equations through an implicit construction proposed by Tsarev [7] For a certain class of ramp-like initial data, Tian [6] has constructed the global solution of the Whitham equations which matches at the phase transition boundaries to the characteristic solution of the i

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Long-Time Asymptotics for the Autocorrelation Function of the Transverse Ising Chain at the Criticaensional lattice. As is well known, the Hamiltonain . can clearly be identified with the transverse Ising model at the critical transverse magnetic field ([LSM]). We will study the long-time behavior of the autocorrelation function .(.) of the first spin component.where . = 1/. is the inverse temper

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Resonances in Multifrequency Averaging Theory,ispersion. The principal term of such asymptotic solutions can be represented in the form.,where ., ., . and ., . are smooth functions and . is 2.-periodic in the argument .. The function (1.1) describes the distribution of wave packets. Such solutions were used in different physical and mechanical