On gauge transformations of Backlund type and higher order nonlinear Schrodinger equations

We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class of Backlund transformations. These transformations satisfy certain reasonable, previously proposed requirements for gauge transformations. Their application to the Schrodinger equation results in higher order partial differential equations. As an example, we derive a general family of sixth-order nonlinear Schrodinger equations, closed under our nonlinear gauge group. We also introduce a new gauge invariant current sigma=rhodelDelta ln rho, where rho=(ψ) over bar psi. We derive gauge invariant quantities, and characterize the subclass of the sixth-order equations that is gauge equivalent to the free Schrodinger equation. We relate our development to nonlinear equations studied by Doebner and Goldin, and by Puszkarz. (C) 2002 American Institute of Physics.