The KdV prolongation algebra

DOI10.1063/1.524442zbMath0453.35073OpenAlexW1973725735MaRDI QIDQ3900423

William F. Shadwick

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1063/1.524442

zbMATH Keywords

conservation lawsLie algebraKorteweg-de Vries equationnilpotent algebraWahlquist-Estabrook prolongation

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Partial differential equations of mathematical physics and other areas of application (35Q99) Continuation and prolongation of solutions to PDEs (35B60)

Related Items (15)

Moving frames and prolongation algebras ⋮ Prolongation theory. A new nonlinear Schrödinger equation ⋮ A nilpotent prolongation of the Robinson–Trautman equation ⋮ Exterior differential expression of the \((1+1)\)-dimensional nonlinear evolution equation with Lax integrability ⋮ Exterior differential systems prolongations and application to a study of two nonlinear partial differential equations ⋮ Coverings and integrable pseudosymmetries of differential equations ⋮ Equations with soliton solutions and the pseudosphere ⋮ Lie algebra computations ⋮ Infinite-dimensional Estabrook–Wahlquist prolongations for the sine-Gordon equation ⋮ GEOMETRIC APPROACHES TO PRODUCE PROLONGATIONS FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS ⋮ Nonlinear evolution equations and nonabelian prolongations ⋮ Non-abelian prolongations and complete integrability ⋮ Nonlocal symmetries of the KdV equation ⋮ A geometric interpretation of prolongation by means of connections ⋮ Prolongations to higher jets of Estabrook-Wahlquist coverings for PDE's

Cites Work

• The soliton connection
• Prolongation structures of nonlinear evolution equations
• A Lie group framework for soliton equations. I. Path independent case
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Geometric Approach to Invariance Groups and Solution of Partial Differential Systems

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