G Kaniadakis and A M Scarfone 2002 J. Phys. A: Math. Gen. 35 1943 doi:10.1088/0305-4470/35/8/311
G Kaniadakis and A M Scarfone
Show affiliationsWe consider systems which conserve the particle number and are described by Schrödinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf-like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature.
03.65.Ge Solutions of wave equations: bound states
70H15 Canonical and symplectic transformations
35Q55 NLS-like (nonlinear Schrödinger) equations (See also 37K10)
Issue 8 (1 March 2002)
Received 23 July 2001, in final form 17 December 2001
Published 15 February 2002
G Kaniadakis and A M Scarfone 2002 J. Phys. A: Math. Gen. 35 1943
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