The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions

The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrödinger equation for several types of nonlocal responses are calculated by Ritz's variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the mth power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the (m+2)th power of its beam width.