| Abstract: | Nonlinear evolution equations are generated which correspond to isospectral differential-matrix eigenvalue problems. Although not discussed here, this procedure is appropriate for the analysis of the initial-value solution by the inverse-scattering method. In the 2 × 2 case the results obtained are consistent with other more general procedures. It yields the sine-Gordon equation, the reduced Maxwell-Bloch equations for self-induced transparency, and also a type of PBBM equation for long nonlinear water waves. In the n × n case, equations are derived corresponding to a new class of triad and multitriad resonant nonlinear interaction of wave envelopes. |
