The Hamilton Cartan formalism for rth-order Lagrangians and the integrability of the KdV and modified KdV equations

DOI10.1007/BF00403242zbMath0473.58012MaRDI QIDQ1158674

William F. Shadwick

Publication date: 1981

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Bäcklund transformationssoliton equationssine-GordonLagrangiansalgebra of conserved chargesHamilton-Cartan formalismalgebra of infinitesimal symmetriesformally completely integrableKorteweg-deVries and Modified Korteweg-deVries equationsPoisson bracket for arbitrary conserved charges

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Exterior differential systems (Cartan theory) (58A15) Partial differential equations of mathematical physics and other areas of application (35Q99) Manifolds and measure-geometric topics (49Q99)

Related Items (3)

Variational principles for second-order quasi-linear scalar equations ⋮ The Hamiltonian structure associated to evolution-type Lagrangians ⋮ The Hamiltonian formulation of regular rth-order Lagrangian field theories

Cites Work

• Noether's theorem and Steudel's conserved currents for the sine-Gordon equation
• Higher-order Hamiltonian formalism in field theory
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System

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