A formula for symmetry recursion operators from non-variational symmetries of partial differential equations

DOI10.1007/s11005-021-01413-1zbMath1482.35022arXiv2004.03743OpenAlexW3164640062WikidataQ115381859 ScholiaQ115381859MaRDI QIDQ2038981

Bao Wang, Stephen C. Anco

Publication date: 7 July 2021

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

Full work available at URL: https://arxiv.org/abs/2004.03743

zbMATH Keywords

symmetryrecursion operatorHamiltonian operatormultiplieradjoint-symmetrysymplectic operatornon-variationalnon-multiplier

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Invariance and symmetry properties for PDEs on manifolds (58J70) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Geometric theory, characteristics, transformations in context of PDEs (35A30) Variational principles and methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K58)

Related Items (4)

Symmetry actions and brackets for adjoint-symmetries. I: Main results and applications ⋮ Symmetry actions and brackets for adjoint-symmetries. II: Physical examples ⋮ Generalized conditional symmetries and pre-Hamiltonian operators ⋮ Conservation laws analysis of nonlinear partial differential equations and their linear soliton solutions and Hamiltonian structures

Cites Work

• An integrable equation with nonsmooth solitons
• Applications of symmetry methods to partial differential equations
• Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with \(p\)-power nonlinearities in two dimensions
• The Korteweg-de Vries equation and beyond
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• An integrable shallow water equation with peaked solitons
• Direct Construction of Conservation Laws from Field Equations
• Generalization of Noether’s Theorem in Modern Form to Non-variational Partial Differential Equations
• Direct construction method for conservation laws of partial differential equations Part II: General treatment
• A general family of multi-peakon equations and their properties
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