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2002•Journal of Qingdao UniversityRequires access

A HIERARCHY OF NEW INTEGRABLE SYSTEMS AND ITS COUPLED BURGERS EQUATIONS HIERARCHY

Xi-Xiang Xu

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Abstract

Based on a new isospectral problem with three potential functions,a new Lax integral hierarchy of evolution equations with an arbitrary function is obtained in this paper.When the potential is put into two special functions,a kind of Burgers equations hierarchy is given.Moreover,its bi Hamiltonian structures of another equations hierarchy are obtained.It is shown that they are integrable in the Liouville's sense.

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What this paper is about

Based on a new isospectral problem with three potential functions,a new Lax integral hierarchy of evolution equations with an arbitrary function is obtained in this paper.When the potential is put into two special functions,a kind of Burgers equations hierarchy is given.Moreover,its bi Hamiltonian structures of another equations hierarchy are obtained.It is shown that they are integrable in the Liouville's sense.

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Available abstract

Based on a new isospectral problem with three potential functions,a new Lax integral hierarchy of evolution equations with an arbitrary function is obtained in this paper.When the potential is put into two special functions,a kind of Burgers equations hierarchy is given.Moreover,its bi Hamiltonian structures of another equations hierarchy are obtained.It is shown that they are integrable in the Liouville's sense.

Key concepts: Isospectral, Integrable system, Hierarchy, Mathematics, Lax pair, Pure mathematics, Hamiltonian system, Mathematical analysis

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