Modified Hamiltonian systems and canonical transformations arising from the relationship between generalized Zakharov–Shabat and energy-dependent Schrödinger operators

DOI10.1063/1.524811zbMath0487.70023OpenAlexW2168934543MaRDI QIDQ3948640

F. Guil Guerrero, Luis Martínez-Alonso

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1063/1.524811

zbMATH Keywords

infinite dimensionalhierarchy of integrable evolution equationsZakharov-Shabat and AKNS equations

Mathematics Subject Classification ID

Hamilton's equations (70H05) First-order nonlinear hyperbolic equations (35L60) General mathematical topics and methods in quantum theory (81Q99) Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics (70H15)

Related Items (4)

Applying supersymmetry to energy dependent potentials ⋮ Exotic wave patterns in Riemann problem of the high‐order Jaulent–Miodek equation: Whitham modulation theory ⋮ On a new hierarchy of Hamiltonian soliton equations ⋮ Systematic method of generating new integrable systems via inverse Miura maps

Cites Work

• Modifying Lax equations and the second Hamiltonian structure
• A new infinite-dimensional Kirillov's structure related with nonlinear evolution equations
• Nonlinear evolution equations associated with energy-dependent Schrödinger potentials
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• A note on Miura’s transformation
• Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
• Factorization of operators I. Miura transformations
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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