Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to …