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.


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