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2011•International Journal of Modern Physics BRequires access

A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY

Fajun Yu

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Abstract

We present a kind of new continuous limits of an integrable coupling system for discrete AKNS hierarchy by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

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What this paper is about

We present a kind of new continuous limits of an integrable coupling system for discrete AKNS hierarchy by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

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Available abstract

We present a kind of new continuous limits of an integrable coupling system for discrete AKNS hierarchy by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit.

Key concepts: Integrable system, Hierarchy, Toda lattice, Coupling (piping), Limit (mathematics), Lattice (music), Mathematics, Lie algebra

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