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Lamé Potentials and the Stationary (m)KdV Hierarchy
Author(s) -
Gesztesy F.,
Weikard R.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951760107
Subject(s) - mathematics , korteweg–de vries equation , hierarchy , kdv hierarchy , context (archaeology) , pure mathematics , function (biology) , mathematical analysis , nonlinear system , physics , paleontology , quantum mechanics , biology , evolutionary biology , economics , market economy
A new method of constructing elliptic finite‐gap solutions of the stationary Korteweg‐de Vries (KdV) hierarchy, based on a theorem due to PICARD , is illustrated in the concrete case of the Lamé‐Ince potentials ‐ s(s + 1) ρ( z ), sε (ρ(.) the elliptic Weierstrass function). Analogous results are derived in the context of the stationary modified Korteweg‐de Vries (mKd V) hierarchy for the first time.