Conditions for a Solitonic Solution of the Doener–Goldin Equation of Quantum Mechanics
Elisabeth C. Caparelli, Salomon Sylvain Mizrahi, V. V. Dodonov
A solitonic solution to the free-particle motion of Doebner–Goldin nonlinear equation is shown to exist under special conditions. For small values of the nonlinearity parameters, the solution is a plane wave modulated by a cos function, and the solitonic one arises when the parameters surpass some critical values. The mean energy of the particle is a conserved quantity and the continuity equation holds. We also verify that there is no nonlinear gauge transformation (in the sense of Ref. 12) that linearizes that equation.
Modern Physics Letters B•Jun 10, 1998•2 citations