Localized nonlinear waves in systems with time- and space-modulated nonlinearities
J. Belmonte-Beitia, V.M. Pérez-García, V. Vekslerchik, V.V. Konotop
Physical Review Letters 100, 164102 (2008).
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr¨odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly non-trivial solutions such as periodic (breathers), resonant or quasiperiodically oscillating solitons. Some implications to the field of matter-waves are also discussed.