Physics – Mathematical Physics
Scientific paper
2006-11-23
Acta Appl. Math. 109 (2010), 315-359
Physics
Mathematical Physics
42 pages, extended version, the group classification of (1+2)-dimensional cubic Schroedinger equations with potentials was add
Scientific paper
10.1007/s10440-008-9321-4
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class of differential equations. Effective new techniques are proposed. Using these, we exhaustively describe admissible point transformations in classes of nonlinear (1+1)-dimensional Schroedinger equations, in particular, in the class of nonlinear (1+1)-dimensional Schroedinger equations with modular nonlinearities and potentials and some subclasses thereof. We then carry out a complete group classification in this class, representing it as a union of disjoint normalized subclasses and applying a combination of algebraic and compatibility methods. Moreover, we introduce the complete classification of (1+2)-dimensional cubic Schroedinger equations with potentials. The proposed approach can be applied to studying symmetry properties of a wide range of differential equations.
Eshraghi Homayoon
Kunzinger Michael
Popovych Roman O.
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