1996/06/05 by D. B. Fairlie, Ian A. B. Strachan, I. A. B. Strachan · 25 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Equivalence (formal languages) #Integrable system #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Quantum chaos and dynamical systems #Toda lattice #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.1088/0266-5611/12/6/006
published in Inverse Problems 12(6), 885-908 (IOP Publishing) · 29 pages, LaTeX
arxiv created 1996/06/05 · openalex publication_date 1996/12/01 · arxiv updated 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields. This symmetry enables formulae normally given implicitly in terms of residues, such as conserved charges and fluxes, to be calculated explicitly. As a corollary of these results the equivalence of the Benney and Toda hierarchies is established. It is further shown that such quantities may be expressed in terms of generalized hypergeometric functions, the simplest example involving Legendre polynomials. These results are then extended to systems derived from a rational Lax function and a logarithmic function. Various reductions are also studied.