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Oscillations and instabilities in near integrable PDE’s. (English) Zbl 0605.35079
Nonlinear systems of partial differential equations in applied mathematics, Proc. SIAM-AMS Summer. Semin., Santa Fe/N.M. 1984, Lect. Appl. Math. 23, Pt. 1, 3-46 (1986).
[For the entire collection see Zbl 0579.00008.]
The authors give general qualitative information about solutions of nonlinear evolutionary partial differential equations which can be obtained from integrable methods. The following topics are treated: propagation of oscillations, coherent structures. Numerical experiments are also presented.
Reviewer: P.Godin

35Q99 Partial differential equations of mathematical physics and other areas of application
35B10 Periodic solutions to PDEs
35B20 Perturbations in context of PDEs
58J50 Spectral problems; spectral geometry; scattering theory on manifolds