Bright and dark sinks-type solitons for the generalized nonlinear Schrödinger equation in polynomial potential in the presence of external source

We theoretically investigate bright and dark sinks-type solitons, a kink and anti-kink solitons, bi-solitons and the pulsed solitons for the generalized nonlinear Schrödinger equation in polynomial potential in the presence of external source. For the polynomial potential, based on some powerful transformation methods with different types of expressions in Jacobi elliptic functions or polynomial functions, soliton have been discovered for the generalized nonlinear Schrödinger equation featuring external potential and source. We systematically investigate the property of sinks and offer an appropriate analytical formula for their shape. These results may be useful to explain some nonlinear wave phenomena in Bose–Einstein condensates, nonlinear optics and physics of plasma.