Spatiotemporally modulated similaritons and composite waves in inhomogeneous system

General and refined spatiotemporal similariton solutions are presented by introducing arbitrary real temporal and spatial modulation functions that construct flexible and controllable relationships among dispersion, nonlinearity and external potential in spatiotemporal modulation inhomogeneous system. The modulated bright similariton (MBS), modulated dark similariton (MDS) and modulated plane wave (MPW) solutions are achieved by a general self-similar transformation method, and modulated dynamics of the MBS, MDS and MPW by choosing Gaussian/periodic temporal function and periodic spatial function. Furthermore, by applying self-similar transformation to M-component spatiotemporal inhomogeneous nonlinear Schrödinger equations, M-component spatiotemporal solutions are obtained and the spatiotemporal modulated properties of 2-component composite waves are studied in detail. The presented results may open many new possibilities for generation and controlling of solitons.