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2008•Modern Physics Letters BRequires access

INTEGRABLE COUPLINGS OF THE (2+1)-DIMENSIONAL Li HIERARCHY AND ITS HAMILTONIAN STRUCTURE AS WELL AS THE MULTI-COMPONENT Li HIERARCHY

Ming Song, Huanhe Dong, Xiuli Xu, HUIJIAN GAO

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Abstract

A (2+1)-dimensional Li hierarchy is generated from one of the reduced equations of self-dual Yang–Mills equations. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable couplings is worked out by using the quadratic-form identity, which is Liouville integrable. Moreover, a corresponding multi-component Li hierarchy is given. The method can be widely applied to other soliton hierarchies.

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What this paper is about

A (2+1)-dimensional Li hierarchy is generated from one of the reduced equations of self-dual Yang–Mills equations. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable couplings is worked out by using the quadratic-form identity, which is Liouville integrable. Moreover, a corresponding multi-component Li hierarchy is given. The method can be widely applied to other soliton hierarchies.

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Available abstract

A (2+1)-dimensional Li hierarchy is generated from one of the reduced equations of self-dual Yang–Mills equations. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable couplings is worked out by using the quadratic-form identity, which is Liouville integrable. Moreover, a corresponding multi-component Li hierarchy is given. The method can be widely applied to other soliton hierarchies.

Key concepts: Integrable system, Hierarchy, Loop algebra, Hamiltonian (control theory), Quadratic equation, Soliton, Mathematical physics, Component (thermodynamics)

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INTEGRABLE COUPLINGS OF THE (2+1)-DIMENSIONAL Li HIERARCHY AND ITS HAMILTONIAN STRUCTURE AS WELL AS THE MULTI-COMPONENT Li HIERARCHY — Research Paper | ScholarLens