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The Korteweg-de Vries equation and beyond. (English) Zbl 0842.58045
The author reviews a new method for linearizing the initial-boundary value problem of the Korteweg-de Vries (KdV) equation on the semi-infinite line for decaying initial and boundary data. The author also presents a novel class of physically important integrable equations. These equations, which include generalizations of the KdV, of the modified KdV, of the nonlinear Schrödinger and of the \(N\)-wave interactions, are as generic as their celebrated counterparts and it appears that they describe certain physical situations more accurately.
Reviewer: Y.Kozai (Tokyo)

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
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