Breather solutions of the generalized nonlinear Schrödinger equation with spatially modulated parameters and a special external potential

By applying the similarity transformation we find analytical solutions of the generalized nonlinear Schrödinger equation with spatially modulated parameters and a special external potential in the form of periodic breathing nonlinear wave packets. These breathers are built by the products of parabolic-cylinder functions and the one-soliton solutions with the continuous-wave background or the second-order soliton solutions of the standard nonlinear Schrödinger equation with constant coefficients. Some examples of such composed solutions possessing applicative potential are given, in which the breathers appear in different forms. The numerical simulations are performed to compare the numerical solution with the analytical solution and to confirm the stability of the breathers found.