The Benney hierarchy and the Dirichlet boundary problem in two dimensions

DOI10.1016/j.physleta.2005.06.027zbMath1194.35477OpenAlexW2160922344MaRDI QIDQ936820

Darren G. Crowdy

Publication date: 20 August 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2005.06.027

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Fundamental solutions to PDEs (35A08) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (3)

Conformal mappings and dispersionless Toda hierarchy. II: General string equations ⋮ Constructing Benney reductions associated with cyclic \((n,s)\) curves ⋮ Conformal mappings and dispersionless Toda hierarchy

Cites Work

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• Laplacian growth and Whitham equations of soliton theory
• Integrable structure of the Dirichlet boundary problem in two dimensions
• Conformal maps and reductions of the Benney equations
• Higher genus hyperelliptic reductions of the Benney equations
• Hele-Shaw flows with time-dependent free boundaries involving a multiply-connected fluid region
• Hyperelliptic reduction of the Benney moment equations
• The initial value problem for reductions of the Benney equations
• Constructing Multiply Connected Quadrature Domains
• Hele Shaw flows with a free boundary produced by the injection of fluid into a narrow channel
• Some Properties of Long Nonlinear Waves
• Genus-Nalgebraic reductions of the Benney hierarchy within a Schottky model
• Conformal maps and integrable hierarchies
• Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell
• Free bosons and tau-functions for compact Riemann surfaces and closed smooth Jordan curves. Current correlation functions.

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