AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schrödinger equations

DOI10.1063/1.3570301zbMath1316.35271OpenAlexW2072396536MaRDI QIDQ5263575

Hong-Gang Luo, Dun Zhao, Wei-Wei Lou, Yu-Juan Zhang

Publication date: 17 July 2015

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

Full work available at URL: https://doi.org/10.1063/1.3570301

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (8)

Multi-soliton management by the integrable nonautonomous nonlinear integro-differential Schrödinger equation ⋮ Damping-like effects in Heisenberg spin chain caused by the site-dependent bilinear interaction ⋮ Explicit solutions and Darboux transformations of a generalized D-Kaup-Newell hierarchy ⋮ A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations ⋮ Darboux transformations of integrable couplings and applications ⋮ A novel non-isospectral hierarchy and soliton wave dynamics for a parity-time-symmetric nonlocal vector nonlinear Gross-Pitaevskii equations ⋮ Traveling-waves and solitons in a generalized time-variable coefficients nonlinear Schrödinger equation with higher-order terms ⋮ Darboux transformation and conservation laws for an inhomogeneous fifth-order nonlinear Schrödinger equation from the Heisenberg ferromagnetism

Cites Work

• Unnamed Item
• Integrability of the Gross-Pitaevskii equation with Feshbach resonance management
• Emergent nonlinear phenomena in Bose-Einstein condensates. Theory and experiment
• Inverse spectral transform analysis of a nonlinear Schrödinger equation with x-dependent coefficients
• On the complete integrability of a nonlinear Schrödinger equation
• Darboux transformations in integrable systems. Theory and their applications to geometry
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Soliton Management in Periodic Systems
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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