Constructing solvable models of vector non-linear Schrodinger equation with balanced loss and gain via non-unitary transformation

We consider vector Non linear Schrodinger Equation (NLSE) with balanced loss gain (BLG), linear coupling (LC) and a general form of cubic nonlinearity. We use a non-unitary transformation to show that the system can be exactly mapped to the same equation without the BLG and LC, and with a modified time-modulated nonlinear interaction. The nonlinear term remains invariant, while BLG and LC are removed completely, for the special case of a pseudo-unitary transformation. The mapping is generic and may be used to construct exactly solvable autonomous as well as non-autonomous vector NLSE with BLG. We present an exactly solvable two-component vector NLSE with BLG which exhibits power-oscillation. An example of a vector NLSE with BLG and arbitrary even number of components is also presented. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

The study utilized a non-unitary transformation to exactly map a vector NLSE with balanced loss gain and linear coupling to the same equation without these effects, but with a modified nonlinear interaction. This generic mapping approach can be used to construct exactly solvable autonomous and non-autonomous vector NLSEs with balanced loss gain. The research presented exactly solvable examples of two-component vector NLSE with balanced loss gain displaying power oscillations, as well as a vector NLSE with an arbitrary even number of components.