Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach
نویسندگان
چکیده
منابع مشابه
Elliptic Algebro-geometric Solutions of the Kdv and Akns Hierarchies – an Analytic Approach
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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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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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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We develop an alternative systematic approach to the AKNS hierarchy based on elementary algebraic methods. In particular, we recursively construct Lax pairs for the entire AKNS hierarchy by introducing a fundamental polynomial formalism and establish the basic algebro-geometric setting including associated BurchnallChaundy curves, Baker-Akhiezer functions, trace formulas, Dubrovin-type equation...
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We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modi-ed Korteweg{de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectr...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1998
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-98-00765-4