Lattice equations, hierarchies and Hamiltonian structures

DOI10.1016/0378-4371(87)90024-0zbMath0694.35188OpenAlexW1969873957MaRDI QIDQ909130

H. W. Capel, G. L. Wiersma

Publication date: 1987

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4371(87)90024-0

zbMATH Keywords

hierarchyKorteweg-de Vries (KdV) equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (14)

The discrete Korteweg-de Vries equation ⋮ A revisit to the ABS H2 equation ⋮ Pentagram-type maps and the discrete KP equation ⋮ Lattice equations, hierarchies and Hamiltonian structures. II: KP-type of hierarchies on 2D lattices ⋮ Lattice equations, hierarchies and Hamiltonian structures. III: The 2D Toda and KP hierarchies ⋮ Lax pairs, symmetries and conservation laws of a differential-difference equation -- Sato's approach ⋮ Direct linearization approach to discrete integrable systems associated with ℤ _𝒩 graded Lax pairs ⋮ Construction of exact solutions for fractional-type difference-differential equations via symbolic computation ⋮ Closed-form modified Hamiltonians for integrable numerical integration schemes ⋮ Integrable mappings and soliton equations. II ⋮ Integrability of reductions of the discrete Korteweg–de Vries and potential Korteweg–de Vries equations ⋮ A variational perspective on continuum limits of ABS and lattice GD equations ⋮ A novel 8-parameter integrable map in R⁴ ⋮ Semi-discrete Lagrangian 2-forms and the Toda hierarchy

Cites Work

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• Expansions over the ‘‘squared’’ solutions and difference evolution equations
• Nonlinear differential difference equations as Backlund transformations
• Nonlinear differential–difference equations and Fourier analysis
• Method for Solving the Korteweg-deVries Equation
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System

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