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A hierarchy of isospectral non-isospectral and its Lax representations

Tan Zhi-hang

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Abstract

A soliton hierarchy of isospectral (λ t=0) and non-isospectral (λ t=λ n) associated with a spectral resembing AKNS spectral problem is constructed by using the Tu Guizhang form.Its Hamilton formulation is established by using the trace identity.By generalizing the results given in reference [2， 3], the author makes it fit the Lax representation of non-isospectral with spectral parameter in characteristic operator, and gives the Lax represontation of soliton hierarchy with isospectral and non-isospectral.

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A soliton hierarchy of isospectral (λ t=0) and non-isospectral (λ t=λ n) associated with a spectral resembing AKNS spectral problem is constructed by using the Tu Guizhang form.Its Hamilton formulation is established by using the trace identity.By generalizing the results given in reference [2， 3], the author makes it fit the Lax representation of non-isospectral with spectral parameter in characteristic operator, and gives the Lax represontation of soliton hierarchy with isospectral and non-isospectral.

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Available abstract

A soliton hierarchy of isospectral (λ t=0) and non-isospectral (λ t=λ n) associated with a spectral resembing AKNS spectral problem is constructed by using the Tu Guizhang form.Its Hamilton formulation is established by using the trace identity.By generalizing the results given in reference [2， 3], the author makes it fit the Lax representation of non-isospectral with spectral parameter in characteristic operator, and gives the Lax represontation of soliton hierarchy with isospectral and non-isospectral.

Key concepts: Isospectral, Hierarchy, Mathematics, Pure mathematics, Spectrum (functional analysis), Operator (biology), TRACE (psycholinguistics), Soliton

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