Algebro-Geometric Finite-Band Solutions of the Ablowitz-Ladik Hierarchy

2006/11/30 by Fritz Gesztesy, Helge Holden, Johanna Michor +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1093/imrn/rnm082

published as Int. Math. Res. Not. 2007, no. 20, Art. ID rnm082, 55 pp · 41 pages

openalex publication_date 2007/09/21 · arxiv created 2007/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a detailed derivation of all complex-valued algebro-geometric finite-band solutions of the Ablowitz–Ladik hierarchy. In addition, we survey a recursive construction of the Ablowitz–Ladik hierarchy and its zero-curvature and Lax formalism.

Citations

• Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz–Ladik Hierarchy

Cited by

• Local Conservation Laws and the Hamiltonian Formalism for the Ablowitz–Ladik Hierarchy
• Algebro-geometric solutions and their reductions for the Fokas-Lenells hierarchy
• The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy