Spatial similaritons in the (2+1)-dimensional inhomogeneous cubic-quintic nonlinear Schrödinger equation

Along the idea of the similarity transformation, analytical spatial similaritons to a (2+1)-dimensional inhomogeneous cubic-quintic nonlinear Schrödinger equation with distributed diffraction and gain are derived when some certain compatibility conditions are satisfied. Based on these exact solutions, we investigate dynamic behaviors of self-similar cnoidal waves and chirped similaritons in the hyperbolically and Gaussian decreasing diffraction waveguides.