Symmetry classification of variable coefficient cubic-quintic nonlinear Schrödinger equations

Abstract

A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrödinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that their symmetry group can be at most four-dimensional in the genuine cubic-quintic nonlinearity. It is only five-dimensional (isomorphic to the Galilei similitude algebra gs(1)) when the equations are of cubic type, and six-dimensional (isomorphic to the Schrödinger algebra sch(1)) when they are of quintic type.

References in corpus (2)

• Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities
• Variable coefficient nonlinear Schrödinger equations with four-dimensional symmetry groups and analysis of their solutions

Cited by in corpus (2)

• Equivalence groupoids and group classification of multidimensional nonlinear Schrödinger equations
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