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On a class of physically important integrable equations. (English) Zbl 1194.35363

Summary: A methodology introduced by Fuchssteiner and the author is used to derive a class of physically important integrable evolution equations. Among these equations are integrable generalizations of the Korteweg-deVries (KdV), of the modified KdV, of the nonlinear Schrödinger (NLS), and of the sine-Gordon equations. The modeling of water waves, as well as general asymptotic considerations, are used to illustrate the occurrence of the generalized modified KdV and NLS equations, respectively.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
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