Symmetry, local linearization, and Gauge classification of the Doebner-Goldin equation

DOI10.1016/0034-4877(96)83634-2zbMath0884.35151arXivquant-ph/9506037OpenAlexW3101043741MaRDI QIDQ1372489

P. Nattermann

Publication date: 13 November 1997

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/9506037

zbMATH Keywords

nonlinear Schrödinger equationsLie symmetriesgauge classificationLie symmetry algebras

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items (6)

Conditional symmetry and spectrum of the one-dimensional Schrödinger equation ⋮ On vertex algebra representations of the Schrödinger-Virasoro Lie algebra ⋮ Is quantum mechanics exact? ⋮ On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin models ⋮ Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations ⋮ Resonance Broadening Theory of Farley-Buneman Turbulence in the Auroral E-Region

Cites Work

• Exact solutions of the general Doebner-Goldin equation
• Evolution equations invariant under two-dimensional space–time Schrödinger group
• On a class of homogeneous nonlinear Schrödinger equations
• On integrable Doebner - Goldin equations
• Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations
• A new class of nonlinear generalizations of the Schrodinger equation
• Properties of nonlinear Schrodinger equations associated with diffeomorphism group representations
• Multidimensional nonlinear Schrodinger equations with exponentially confined solutions
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