Noether's theorem and Steudel's conserved currents for the sine-Gordon equation

DOI10.1007/BF00316680zbMath0444.58011MaRDI QIDQ1144828

William F. Shadwick

Publication date: 1980

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

zbMATH Keywords

extended Hamilton-Cartan formalism for regular first-order Lagrangiansformal complete integrability of the sine-Gordon equationsine-Gordon Bäcklund transformations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

The Hamilton Cartan formalism for rth-order Lagrangians and the integrability of the KdV and modified KdV equations, On the permutability of Bäcklund transformations. I: Infinitesimal Bäcklund transformations of the sine-Gordon equation, Higher-order conservation laws for the nonlinear Poisson equation via characteristic cohomology, The Hamiltonian formulation of regular rth-order Lagrangian field theories, Case's conjecture on Bäcklund transformations and conservation laws, Similarity solutions of nonlinear Dirac equations and conserved currents

Cites Work

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• The Hamilton-Cartan formalism for higher order conserved currents. I: Regular first order Lagrangians
• Local jet bundle formulation of Bäcklund transformations. With applications to non-linear evolution equations
• Noether equations and conservation laws
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws