Spatial bright and dark similaritons on cnoidal wave backgrounds in 2D waveguides with different distributed transverse diffractions

We discuss the (2+1)-dimensional nonlinear Schrödinger equation with different distributed transverse diffractions in waveguides via a similarity transformation method and obtain exact solutions including bright and dark similariton solutions on cnoidal wave backgrounds. Moreover, the compression and stretching problems of these similariton solutions in a diffraction decreasing waveguide and constant system are, respectively, investigated. These results are potentially useful for future experiments and application of similaritons and solitons for long-distance optical communications.