Higher symmetries and exact solutions of linear and nonlinear Schr{umlt o}dinger equation

Journal Article · Fri Oct 31 23:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532180· OSTI ID:587650

Fushchych, W I; Nikitin, A G ^[1]

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1. Institute of Mathematics, National Academy of Sciences of Ukraina, 3 Tereshchenkivska Street, Kyiv-4, (Ukraina)

A new approach for the analysis of partial differential equations is developed which is characterized by a simultaneous use of higher and conditional symmetries. Higher symmetries of the Schr{umlt o}dinger equation with an arbitrary potential are investigated. Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlev{acute e}, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Schr{umlt o}dinger equations. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 587650
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRA
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
SCHROEDINGER EQUATION
SYMMETRY