The Hamiltonian structures of the nonlinear Schrödinger equation in the classical limit

DOI10.1063/1.527553zbMath0621.76017OpenAlexW2080543835MaRDI QIDQ3758412

John M. Verosky

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1063/1.527553

zbMATH Keywords

nonlinear Schrödinger equationKorteweg-de Vries equationbi-Hamiltonian structureclassical limitshallow water wave equationscompletely integrable Hamiltonian systemMadelung's hydrodynamical variables

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99) Hamiltonian and Lagrangian mechanics (70H99)

Cites Work

• Modifying Lax equations and the second Hamiltonian structure
• Mathematics of dispersive water waves
• Higher-order symmetries of the compressible one-dimensional isentropic fluid equations
• On the Hamiltonian structure of evolution equations
• Evolution equations possessing infinitely many symmetries
• A simple model of the integrable Hamiltonian equation
• Korteweg-de Vries Equation and Generalizations. IV. The Korteweg-de Vries Equation as a Hamiltonian System

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