Spatiotemporal soliton solutions in three dimensional combined linear-harmonic potentials with varying sources

We obtain spatiotemporal soliton solutions to the generalized nonlinear Schrödinger equation in three dimensional combined linear-harmonic potentials with varying sources by numerical and analytical methods. Three physically relevant examples, the trigonometric profile, Sinc profile, and Airy profile, are investigated to demonstrate the properties of spatiotemporal solutions for different functional forms of diffraction and potential strength. The results demonstrate that the structures of these spatiotemporal soliton solutions can be effectively manipulated by appropriately tuning the diffraction, potential strength, and source term. Numerical simulations demonstrate the stable propagation of solutions and their robustness against disturbances under the constraint condition.