Compactons in nonlinear Schrödinger lattices with strong nonlinearity management

The existence of compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged discrete nonlinear Schrödinger equation, the resulting effective interwell tunneling depends on the modulation parameters and on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multisite stable discrete compactons in nonlinear optical waveguide and Bose-Einstein condensate arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.