Hierarchy of symplectic forms for the Schrödinger and the Dirac equations on a line

DOI10.1007/BF01375613zbMath0511.35072MaRDI QIDQ1838643

A. G. Reyman, Petr P. Kulish

Publication date: 1983

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

conservation lawsSchrödinger equationHamiltoniansDirac equationKorteweg-de Vries equationnonlinear evolution equationsinverse scattering problemhierarchy of symplectic forms

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Scattering theory for PDEs (35P25) Hyperbolic conservation laws (35L65) Schrödinger operator, Schrödinger equation (35J10) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (1)

Solutions of string, vortex, and anyon types for the hierarchy of the nonlinear Schrödinger equation

Cites Work

• On the complete integrability of a nonlinear Schrödinger equation
• Hamiltonian systems connected with the Dirac equation
• The Hamiltonian system connected with the equation u//(xi,nu)+sin u=0
• Complete Integrability of Nonlinear Evolution Equations
• Korteweg‐devries equation and generalizations. VI. methods for exact solution
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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