Evolution equations invariant under two‐dimensional space–time Schrödinger group

Autor:	G. Rideau, Pavel Winternitz
Rok vydání:	1993
Předmět:	Schrödinger group Partial differential equation Lie group Statistical and Nonlinear Physics Symmetry group Schrödinger equation symbols.namesake Lie algebra symbols Vector field Invariant (mathematics) Mathematical Physics Mathematical physics Mathematics
Zdroj:	Journal of Mathematical Physics. 34:558-570
ISSN:	1089-7658 0022-2488
DOI:	10.1063/1.530261
Popis:	The most general second order evolution equation ψt+F(x,t,ψψ*,ψx,ψx*,ψxx, ψxx*)=0, invariant under the Galilei, Galilei‐similitude, and Schrodinger 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 Schrodinger invariant equations, in particular, are found integrable equations, linearizable by contact transformations.
Databáze:	OpenAIRE
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