Exact similariton solution families and diverse composite waves in coherently coupled inhomogeneous systems

Seeking analytical solutions of nonlinear Schrödinger (NLS)-like equations remains an open topic. In this paper, we revisit the general inhomogeneous nonautonomous NLS (inNLS) equation and report on exact similaritons under generic constraint relationships by proposing a novel generic self-similar transformation, which implies that there exist a rich variety of highly controllable solution families for inhomogeneous systems. As typical examples, richly controllable behaviors of the self-similar soliton (SS), self-similar Akhmediev breather (SAB), self-similar Ma breather (SMB), and self-similar rogue wave (SRW) are presented in a periodic distribution nonlinear system. With the aid of a linear transformation, these novel similariton solutions are deployed as a basis for constructing two-component composite solutions to a pair of coherently coupled inNLS equations including four-wave mixing. The diverse composite waves that emerge, including SS–SS, SAB–SMB, and SRW–SRW families, are investigated in some detail. The family of similariton solutions presented here may prove significance for designing the control and transmission of nonlinear waves.