New form of collective particle-like excitations in one-dimensional systems with resonance interaction

Soliton-like solutions are obtained and investigated for the “perturbed” Schrödinger equation with cubic nonlinearity, which describes many phenomena in the theory of the condensed state. It is shown that there exists an entire class of solutions that cannot be obtained by the standard procedure of expansion with respect to a small parameter, this being so even in the framework of the inverse scattering technique. The explicit form of two such solutions is given, which immediately demonstrates the validity of the above assertion.