Exact solitons in three-dimensional weakly nonlocal nonlinear time-modulated parabolic law media

• The three-dimensional nonlocal nonlinear Schrodinger equation is studied analytically.
• Explicit solutions are constructed by using the Jacobian elliptic equations expansion method.
• The 3D nonlocal spatial bright and dark optical solitons are found.

The three-dimensional (3D) nonlocal nonlinear Schrödinger equation (NNLSE) with time-dependent parabolic law nonlinearity and an external potential, describes the propagation of an optical pulse in the weakly nonlocal nonlinear parabolic law media, has been studied analytically. Explicit solutions are constructed by using the Jacobian elliptic equations (JEEs) expansion method. The 3D nonlocal spatial bright and dark optical solitons have been found.