2012/12/10 by Guo Liang, Qi Guo, Liang, Guo +1 · 1 citation
Mathematics · Physics and Astronomy · #Classical Physics (physics.class-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #nlin.SI #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1212.1955
11 pages, no figures
arxiv created 2012/12/10 · openalex publication_date 2012/12/10 · arxiv updated 2012/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differential system. It is pointed out for the first time that the number of the canonical equations for the first-order differential system is half of that for the second-order differential system. The nonlinear Schrödinger equation, a universal first-order differential system, can be expressed with the new canonical equations in a consistent way.