On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin models

DOI10.1016/S0034-4877(00)89037-0zbMath0970.81024OpenAlexW2093677800MaRDI QIDQ5938856

Olena Roman, Renat Zhdanov

Publication date: 7 August 2001

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

Full work available at URL: https://doi.org/10.1016/s0034-4877(00)89037-0

zbMATH Keywords

Galilei-invariant

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) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Invariance and symmetry properties for PDEs on manifolds (58J70)

Related Items

Symmetry classification of KdV-type nonlinear evolution equations, Group classification of (1+1)-dimensional Schrödinger equations with potentials and power nonlinearities, Lie group classification of the \(N\)-th-order nonlinear evolution equations, Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations, Algebraic method for group classification of \((1+1)\)-dimensional linear Schrödinger equations, Nonlocal symmetries of systems of evolution equations, Symmetry classification of variable coefficient cubic-quintic nonlinear Schrödinger equations, Admissible transformations and normalized classes of nonlinear Schrödinger equations, Group classification of differential-difference equations: low-dimensional Lie algebras, Classification of local and nonlocal symmetries of fourth-order nonlinear evolution equations, Galilei symmetries of KdV-type nonlinear evolution equations, Preliminary group classification of quasilinear third-order evolution equations, Preliminary group classification of a class of fourth-order evolution equations, Square-integrable solutions to a family of nonlinear Schrödinger equations from nonlinear quantum theory

Cites Work

• Symmetry, local linearization, and Gauge classification of the Doebner-Goldin equation
• Low-dimensional real Lie algebras
• Evolution equations invariant under two-dimensional space–time Schrödinger group
• Nonlinear evolution equations invariant under the Schrödinger group in three-dimensional spacetime
• On integrable Doebner - Goldin equations
• Group classification of heat conductivity equations with a nonlinear source
• On New Representations of Galilei Groups
• Properties of nonlinear Schrodinger equations associated with diffeomorphism group representations
• Multidimensional nonlinear Schrodinger equations with exponentially confined solutions
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