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Nonlinear-evolution equations of physical significance. (English) Zbl 1243.35143
Summary: We present the inverse scattering method which provides a means of solution of the initial-value problem for a broad class of nonlinear evolution equations. Special cases include the sine-Gordon equation, the sinh-Gordon equation, the Benney-Newell equation, the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, and generalizations.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
81Q05Closed and approximate solutions to quantum-mechanical equations
37K15Integration of completely integrable systems by inverse spectral and scattering methods