Three-dimensional Hermite-Bessel solitons in strongly nonlocal media with variable potential coefficients

We solve the three-dimensional nonlinear Schrodinger equation with variable parabolic potential coefficients in strongly nonlocal nonlinear media. Exact analytical solutions in the form of self-similar waves, namely the Hermite-Bessel solitons, are found. Higher-order Hermite-Bessel solitons, which can exist in various forms such as the three-dimensional vortex solitons and the multipole solitons are also discussed. To ascertain the stability of these analytical solutions during evolution, numerical simulations have been performed. (c) 2013 Elsevier B.V. All rights reserved.