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Some Higher‐Order Nonlinear Evolution Equations

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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.
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Document Type: Research Article

Affiliations: Rutgers University

Publication date: December 1, 1975

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