Dispersionful analogues of Benney's equations and N -wave systems

1995/10/11 by Benjamin Enriquez, B. Enriquez, A. Yu. Orlov +2 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #hep-th #nlin.SI #solv-int

paper · pdf · doi:10.1088/0266-5611/12/3/005

12 pages, latex, no figures

arxiv created 1995/10/11 · openalex publication_date 1996/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We recall Krichever's construction of additional flows to Benney's hierarchy, attached to poles at finite distance of the Lax operator. Then we construct a `dispersionful' analogue of this hierarchy, in which the role of poles at finite distance is played by Miura fields. We connect this hierarchy with N-wave systems, and prove several facts about the latter (Lax representation, Chern - Simons-type Lagrangian, connection with Liouville equation, -functions).

Citations

• Commutative Ordinary Differential Operators
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory

Cited by

• On the Benney hierarchy: free energy, string equation and quantization
• Darboux Transformations for (2+1)-Dimensional Extensions of the KP Hierarchy
• Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations
• The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies