Soliton-like excitations in weakly dispersive media

We consider the question of the possible existence of two-parameter envelope solitons in weakly dispersive media with an acoustic spectrum of linear waves. We propose an asymptotic procedure for finding such soliton solutions in the one-dimensional case and demonstrate the proposed method in the example of the modified Boussinesq equation. We study the question of nonlinear multidimensional localization of excitations in weakly dispersive media with an acoustic spectrum of linear waves.