A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy
نویسندگان
چکیده
منابع مشابه
A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy
Here ~9(x):p(x; wl,w3) denotes the elliptic Weierstrass function with fundamental periods 2wl and 2w3 (Im(w3/Wl)#0). In the special case where Wl is real and w3 is purely imaginary, the potential q(x) in (1.1) is real-valued and Ince's striking result [51], in modern spectral-theoretic terminology, yields that the spectrum of the unique self-adjoint operator associated with the differential exp...
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An explicit characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy is presented. More precisely, we show that a pair of elliptic functions (p, q) is an algebro-geometric AKNS potential, that is, a solution of some equation of the stationary AKNS hierarchy, if and only if the associated linear differential system JΨ +QΨ = EΨ, where J = (
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We provide an overview of elliptic algebro-geometric solutions of the KdV and AKNS hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. Our treatment includes an effective characterization of all stationary elliptic KdV and AKNS solutions based on a theory developed by Hermite and Picard.
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1998
ISSN: 0001-5962
DOI: 10.1007/bf02392748