Darboux transformation for the non-isospectral AKNS hierarchy and its asymptotic property
نویسندگان
چکیده
منابع مشابه
Darboux Transformation for the Non-isospectral AKNS Hierarchy and Its Asymptotic Property
In this article, the Darboux transformation for the non-isospectral AKNS hierarchy is constructed. We show that the Darboux transformation for the non-isospectral AKNS hierarchy is not an auto-Bäcklund transformation, because the integral constants of the hierarchy will be changed after the transformation. The transform rule of the integral constants will be also derived. By this means, the sol...
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A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS flows. These nonlinearized Lax systems also...
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A GBDT version of the Bäcklund–Darboux transformation is constructed for a non-isospectral canonical system, which plays essential role in the theory of random matrix models. The corresponding Riemann–Hilbert problem is treated and some explicit formulas are obtained. A related inverse problem is formulated and solved.
متن کاملNon-isospectral Multi-component AKNS Equations and New Integrable Couplings
Positive and negative hierarchies of non-isospectral multi-component AKNS equations are derived from an arbitrary order matrix spectral problem. Moreover, new non-isospectral multi-component integrable couplings of the resulting soliton hierarchies are constructed by enlarging the associated matrix spectral problem. Mathematics Subject Classification: 35Q58
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allowed for determined boundary conditions corresponding to the standard potential . With the very useful Darboux transformation (DT) [3-6] is possible to generalize any specific standard potential and thus generate new interaction models with the same energy levels. The DT is related to the Sturm-Liouville theory [7-10], and it is easy to see the implicit presence of DT in supersymmetric quant...
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2008
ISSN: 0375-9601
DOI: 10.1016/j.physleta.2008.06.072