Non-Noether symmetries in integrable models

2003/07/31 by George Chavchanidze
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.DS #math.MP #math.SG #msc:35A30 #msc:53Z05 #msc:58J70 #msc:70H06 #msc:70H33

paper · pdf · doi:10.1088/0305-4470/37/6/020

published as J. Phys. A: Math. Gen. 37 (2004) 2253--2260 · LaTeX 2e article, 10 pages, no figures

arxiv created 2003/08/13 · openalex publication_date 2004/01/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

In the present paper the non-Noether symmetries of the Toda model, nonlinear Schrödinger equation and Korteweg–de Vries equations (KdV and mKdV) are discussed. It appears that these symmetries yield the complete sets of conservation laws in involution and lead to the bi-Hamiltonian realizations of the above-mentioned models.

Citations

• Non-Noether symmetries and their influence on phase space geometry

Related

• Non-Noether symmetries in Hamiltonian Dynamical Systems
• Non-Noether symmetries and their influence on phase space geometry
• Remark on conservation laws associated with non-Noether symmetries
• Bi-Hamiltonian structure as a shadow of non-Noether symmetry
• Nonisospectral symmetries of the KdV equation and the corresponding symmetries of the Whitham equations