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arXiv · 1708.06841

The strict AKNS hierarchy: its structure and solutions

Gerard Helminck
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Abstract

In this paper we discuss an integrable hierarchy of compatible Lax equations that is obtained by a wider deformation of a commutative algebra in the loop space of ${\rm sl}_{2}$ than that in the AKNS-case and whose Lax equations are based on a different decomposition of this loop space. We show the compatibility of these Lax equations and that they are equivalent to a set of zero curvature relations. We present a linearization of the system and conclude by giving a wide construction of solutions of this hierarchy.

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Gerard Helminck. 2017-08-22. The strict AKNS hierarchy: its structure and solutions. https://doi.org/10.1155/2016%2F3649205

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