A new 4 × 4 AKNS spectral problem and its associated integrable decomposition of the AKNS equation

Abstract

A new approach to construct a new 4 × 4 matrix spectral problem from a normal 2 sx 2 matrix spectral problem is presented. AKNS spectral problem is discussed as an example. The isospectral evolution equation of the new 4 × 4 matrix spectral problem is nothing but the famous AKNS equation hierarchy. With the aid of the binary nonlinearization method, the authors get new integrable decompositions of the AKNS equation. In this process, the r-matrix is used to get the result.

Keywords

Spectral problem / Integrable decomposition / r-matrix

References

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