Symmetries and reductions of nonlinear Schrödinger equations of Doebner-Goldin type

DOI10.1016/0034-4877(96)83513-0zbMath0884.35147OpenAlexW2116987070MaRDI QIDQ1372435

P. Nattermann, V. Chopyk, Wolfgang Scherer, W. I. Fushchich

Publication date: 1995

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

Full work available at URL: https://doi.org/10.1016/0034-4877(96)83513-0

zbMATH Keywords

explicit solutionsreductionsymmetric algebrasnonlinear Schrödinger equationsmaximal symmetry algebras

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Integration on manifolds; measures on manifolds (58C35)

Related Items (8)

Fractional Galilean symmetries ⋮ Solutions of the relativistic nonlinear wave equation by solutions of the nonlinear Schrödinger equation ⋮ Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations ⋮ On vertex algebra representations of the Schrödinger-Virasoro Lie algebra ⋮ Possible central extensions of non-relativistic conformal algebras in 1+1 ⋮ Admissible transformations and normalized classes of nonlinear Schrödinger equations ⋮ Logarithmic correlators in nonrelativistic conformal field theory ⋮ Resonance Broadening Theory of Farley-Buneman Turbulence in the Auroral E-Region

Cites Work

• Modulational instabilities and soliton solutions of a generalized nonlinear Schrodinger equation
• Evolution equations invariant under two-dimensional space–time Schrödinger group
• Properties of nonlinear Schrodinger equations associated with diffeomorphism group representations
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