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A New Approach to the Boussinesq Hierarchy
Author(s) -
Dickson Ronnie,
Gesztesy Fritz,
Unterkofler Karl
Publication year - 1999
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.19991980105
Subject(s) - mathematics , hierarchy , dirichlet distribution , formalism (music) , pure mathematics , trace (psycholinguistics) , algebraic number , algebra over a field , polynomial , mathematical analysis , art , musical , linguistics , philosophy , economics , market economy , visual arts , boundary value problem
Abstract We develop a new systematic approach to the Boussinesq (Bsq) hierarchy based on elementary algebraic methods. In particular, we recursively construct Lax pairs for the Bsq hierarchy by introducing a fundamental polynomial formalism and establish the basic algebro ‐geometric setting including associated Burchnall ‐ Chaundy curves, Baker ‐ Akhiezer functions, trace formulas, and Dubrovin ‐ type equations for Dirichlet and Neumann divisors.