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A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA

Yan Key

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Abstract

In this paper,an isospectral problem with five potentials is investigated in loop algebra A_2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained.And then by fixing the five arbitrary functions to be certain functions and using the trace identity,the generalized Hamiltonian structure of the hierarchy of evolution equations is given.It is shown that this hierarchy of equations is Liouville integrable.Finally some special cases of the isospectral problem are also given.

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What this paper is about

In this paper,an isospectral problem with five potentials is investigated in loop algebra A_2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained.And then by fixing the five arbitrary functions to be certain functions and using the trace identity,the generalized Hamiltonian structure of the hierarchy of evolution equations is given.It is shown that this hierarchy of equations is Liouville integrable.Finally some special cases of the isospectral problem are also given.

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Available abstract

In this paper,an isospectral problem with five potentials is investigated in loop algebra A_2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained.And then by fixing the five arbitrary functions to be certain functions and using the trace identity,the generalized Hamiltonian structure of the hierarchy of evolution equations is given.It is shown that this hierarchy of equations is Liouville integrable.Finally some special cases of the isospectral problem are also given.

Key concepts: Isospectral, Integrable system, Mathematics, Loop algebra, Hierarchy, Algebra over a field, Lax pair, Pure mathematics

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A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA — Research Paper | ScholarLens