# Non-linear Schr$\ddot{o}$dinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction

@inproceedings{Ghosh2021NonlinearSE, title={Non-linear Schr\$\ddot\{o\}\$dinger equation with time-dependent balanced loss-gain and space-time modulated non-linear interaction}, author={Supriyo Ghosh and Pijush K. Ghosh}, year={2021} }

We consider a class of one dimensional vector Non-linear Schrödinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of the Schrödinger field. The solvability of the generic system is investigated for various combinations of time modulated LC and BLG terms, space-time dependent strength of the nonlinear interaction and complex potential. We use a non-unitary transformation followed by a reformulation of the differential…

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