Abstract
Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation andr-matrix are also given in this paper.
Highlights
The inverse scattering method provides us with a powerful tool to generate multicomponent soliton equations
We show that the constrained N copies of systems (7) and (27) are super Hamiltonian systems (32) and (37)
We considered a Bargmann symmetry constraint (31)
Summary
The inverse scattering method provides us with a powerful tool to generate multicomponent soliton equations. Monononlinearization of Lax pair is a method to obtain finite-dimensional integrable Hamiltonian system, which was firstly proposed by Cao in [5]. The main idea of monononlinearization includes the following three aspects They find a symmetry constraint between potential and eigenfunctions. Substituting the symmetry constraint into the spectral problem, they obtain constrained finite-dimensional system. They show that obtained constrained system is Hamiltonian system and completely integrable in the Liouville sense. We can apply both monononlinearization and binary-nonlinearization to the even-dimensional spectral problem. Owing to one-component super integrable system which is associated with a 3 × 3 spectral matrix, we just consider binary-nonlinearization in our previous papers [15,16,17].
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