Evolution equations invariant under two-dimensional space–time Schrödinger group
| ISSN: |
1089-7658
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|---|---|
| Source: |
AIP Digital Archive
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| Topics: |
Mathematics
Physics
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| Notes: |
The most general second order evolution equation ψt+F(x,t,ψψ*,ψx,ψx*,ψxx, ψxx*)=0, invariant under the Galilei, Galilei-similitude, and Schrödinger groups in two dimensions, is constructed. A preliminary step is a classification of all possible realizations of the corresponding Lie algebras of vector fields in R2×C parametrized by x, t, ψ, and ψ*. Applications of this study include the investigation of nonlinear alternatives to quantum mechanics and nonrelativistic classical field theories. Among the Schrödinger invariant equations, in particular, are found integrable equations, linearizable by contact transformations.
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| Type of Medium: |
Electronic Resource
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| URL: |